Static Friction - Revision history

Khacminhdau: remove image not loading

2026-04-28T21:55:40Z

remove image not loading

← Older revision		Revision as of 17:55, 28 April 2026
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	<br><b>1.</b> If the weight is doubled, the friction also doubles.		<br><b>1.</b> If the weight is doubled, the friction also doubles.
	<br><b>2.</b> The contact area does not affect friction.		<br><b>2.</b> The contact area does not affect friction.

	~~[[File:davincifriction.jpg\|400px]]~~

	==Connectedness==		==Connectedness==

Khacminhdau: added history section

2026-04-28T21:42:56Z

added history section

← Older revision		Revision as of 17:42, 28 April 2026
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	This page defines and describes static friction. Some of the information presented on this page is also present on the [[Friction]] or [[Rolling Motion]] page.		This page defines and describes static friction. Some of the information presented on this page is also present on the [[Friction]] or [[Rolling Motion]] page.

			<b>Khac Minh Dau SPRING 2026</b>

	==The Main Idea==		==The Main Idea==
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	<math>F_A = \sqrt{(\mu_s * mg - F_B\sin\theta)^2 - (F_B\cos\theta)^2}</math>		<math>F_A = \sqrt{(\mu_s * mg - F_B\sin\theta)^2 - (F_B\cos\theta)^2}</math>

			==History==
			The study of friction, now known as Tribology, began with the experiments of Leonardo Da Vinci (1452–1519), the influential painter, sculptor, architect, and scientist of the Renaissance period. His notebook contains drawings of his experiments and details some fundamental laws of friction:
			<br><b>1.</b> If the weight is doubled, the friction also doubles.
			<br><b>2.</b> The contact area does not affect friction.

			[[File:davincifriction.jpg\|400px]]

	==Connectedness==		==Connectedness==

YorickAndeweg: /* A Mathematical Model */

2019-08-02T18:26:45Z

A Mathematical Model

← Older revision		Revision as of 14:26, 2 August 2019
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	where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.		where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.

			This formula may also be written

			<math>F_s \leq \mu_s * N</math>.

	For problems involving rolling objects, the static friction usually does not reach its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].		For problems involving rolling objects, the static friction usually does not reach its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].

YorickAndeweg: /* Static Friction on Rolling Objects */

2019-07-10T20:20:07Z

Static Friction on Rolling Objects

← Older revision		Revision as of 16:20, 10 July 2019
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	Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.		Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.

	For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the object to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.		For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the object to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the static friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.

	For more information, see [[Rolling Motion]].		For more information, see [[Rolling Motion]].

YorickAndeweg: /* A Mathematical Model */

2019-07-09T18:06:57Z

A Mathematical Model

← Older revision		Revision as of 14:06, 9 July 2019
Line 21:		Line 21:
	where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.		where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.

	~~Often for~~ problems involving rolling objects, the static friction ~~never reaches~~ its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].		For problems involving rolling objects, the static friction usually does not reach its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].

	===A Computational Model===		===A Computational Model===

YorickAndeweg at 17:50, 9 July 2019

2019-07-09T17:50:21Z

← Older revision		Revision as of 13:50, 9 July 2019
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	This page defines and describes static friction. Some of the information presented on this page is also present on the [[Friction]] page.		This page defines and describes static friction. Some of the information presented on this page is also present on the [[Friction]] or [[Rolling Motion]] page.

	==The Main Idea==		==The Main Idea==

YorickAndeweg: /* Static Friction on Rolling Objects */

2019-07-09T17:43:12Z

Static Friction on Rolling Objects

← Older revision		Revision as of 13:43, 9 July 2019
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	Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.		Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.

	For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the ~~wheel~~ to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.		For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the object to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.

	For more information, see [[Rolling Motion]].		For more information, see [[Rolling Motion]].

YorickAndeweg: /* A Mathematical Model */

2019-07-09T16:18:37Z

A Mathematical Model

← Older revision		Revision as of 12:18, 9 July 2019
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	where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.		where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.

	Often for problems involving rolling ~~friction~~, the static friction never reaches its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].		Often for problems involving rolling objects, the static friction never reaches its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].

	===A Computational Model===		===A Computational Model===

YorickAndeweg: /* Rolling Friction */

2019-07-09T16:17:49Z

Rolling Friction

← Older revision		Revision as of 12:17, 9 July 2019
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	Static friction is a type of [[Friction]] that occurs between two touching objects that <b>are not</b> moving with respect to each other at their point of contact. When two objects touch each other and there is no sliding between their surfaces of contact, they exert static friction forces on each other. The static friction force acting on each object opposes any force that would cause it to slide relative to the other object. For example, consider a heavy dresser at rest on the floor. If a child pushes against the side of the dresser in an attempt to slide it, that exerts a force on the dresser, but the ground would exert on it an equal and opposite static friction force that balances the force exerted by the child, so the dresser stays at rest. The static friction force can take on whatever direction and magnitude necessary to balance an external net force that threatens to cause sliding motion between two surfaces. However, the magnitude of the static friction force is limited by a maximum value. If the external force becomes strong enough, the static friction force can be overcome and the surfaces can begin to slide, at which point the friction between the objects becomes [[Kinetic Friction]]. For example, now consider an adult pushing against the same heavy dresser. The adult can exert a stronger force than the child, and if it exceeds the maximum possible static friction force, the dresser can be set into motion and slid across the floor.		Static friction is a type of [[Friction]] that occurs between two touching objects that <b>are not</b> moving with respect to each other at their point of contact. When two objects touch each other and there is no sliding between their surfaces of contact, they exert static friction forces on each other. The static friction force acting on each object opposes any force that would cause it to slide relative to the other object. For example, consider a heavy dresser at rest on the floor. If a child pushes against the side of the dresser in an attempt to slide it, that exerts a force on the dresser, but the ground would exert on it an equal and opposite static friction force that balances the force exerted by the child, so the dresser stays at rest. The static friction force can take on whatever direction and magnitude necessary to balance an external net force that threatens to cause sliding motion between two surfaces. However, the magnitude of the static friction force is limited by a maximum value. If the external force becomes strong enough, the static friction force can be overcome and the surfaces can begin to slide, at which point the friction between the objects becomes [[Kinetic Friction]]. For example, now consider an adult pushing against the same heavy dresser. The adult can exert a stronger force than the child, and if it exceeds the maximum possible static friction force, the dresser can be set into motion and slid across the floor.

	===Rolling ~~Friction~~===		===Static Friction on Rolling Objects===

	Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.		Friction is responsible for the rolling of round objects. When this rolling happens without slipping, the friction is static. Consider a wheel rolling without slipping across the ground. At a glance, it may seem like the friction between the wheel and the ground should be kinetic because the center of the wheel moves relative to the ground. However, to determine the type of friction acting between the wheel and the ground, one must look at the point of contact between them. The point of contact between the wheel and the ground occurs on the edge of the wheel on its lowest point, which is not moving relative to the ground. The point of contact between the wheel and the ground constantly changes but does not slide.

	For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the wheel to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.		For an object rolling at a constant speed, the magnitude of the static friction force is 0 because there are no forces threatening to cause the wheel to slip. For an accelerating rolling object, however, such as a disk rolling down a ramp, the friction force has a nonzero magnitude to prevent the disk from slipping. Without this friction force, a disk placed on a ramp would simply slide down without rotating. It is important to ask oneself whether the static friction force acting on an accelerating rolling object is capable of doing work. The answer depends on whether the rolling object is modeled as a [[Point Particle System]] or a [[Real System]]. If the system is treated as a point particle, the static friction force is treated as though it acts on the particle's center of mass. It is therefore exerted over a distance and does work, affecting the object's total kinetic energy. If the system is treated as a real object, the static friction force is recognized as acting on the object's stationary edge, and therefore does no work. For the real system, the object's total kinetic energy would be the same even if the static friction force at its edge were absent. The only difference is that now some of its kinetic energy is rotational rather than translational. Point particles cannot have rotational kinetic energy, so the static friction force is treated as though it does work to account for the difference in total kinetic energy.

			For more information, see [[Rolling Motion]].

	===A Mathematical Model===		===A Mathematical Model===

YorickAndeweg: /* A Mathematical Model */

2019-07-09T16:16:57Z

A Mathematical Model

← Older revision		Revision as of 12:16, 9 July 2019
Line 19:		Line 19:
	where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.		where <math>\mu_s</math> is the coefficient of static friction of the objects and <math>N</math> is the normal force between the objects. <math>\mu_s</math> is a property of the materials of the surfaces in contact and is usually less than 1. <math>\mu_s</math> has no units because it is a ratio of one force to another. For any given pair of surfaces, their <math>\mu_s</math> value is greater than their <math>\mu_k</math> value.

	Often for problems involving rolling friction, the static friction never reaches its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For ~~such problems, you may be asked to find some unknown quantity, such as the acceleration of a disk rolling down a ramp, which may seem difficult if the value~~ of ~~the friction force is unknown. To solve such a~~ problem, a system of equations should be devised, where one equation relates the friction force to the translational acceleration of the disk and another equation relates the friction force to the rotational acceleration of the disk. For more information, see [[Rolling Motion]].		Often for problems involving rolling friction, the static friction never reaches its maximum allowed by the formula above. In fact, you may not be told the value the coefficient of static friction, only that it is high enough to prevent the object from slipping. For more information about this type of problem, see [[Rolling Motion]].

	===A Computational Model===		===A Computational Model===