Question 1

If an object remains at rest,then the sum of both the external torques and the external forces on the object must be zero.

Accepted Answer

This statement is in accordance with Newton's First Law of Motion, which states that an object at rest will remain at rest unless acted upon by an external force. If the net external torque and force on an object at rest are both zero, then there is no external force to cause the object to move, and it will remain at rest.

Question 2

If the sum of the external forces on an object is zero,then the sum of the external torques on it must also be zero.

Accepted Answer

The sum of the external forces being zero only ensures that the object's linear motion is not changing (i.e., it is either at rest or moving with constant velocity). However, the sum of the external torques can be non-zero if they are applied in such a way that they cause the object to rotate, even when the net external force is zero. This is because torque depends not only on the force but also on the distance from the pivot point and the angle at which the force is applied.

Question 3

Two equal-magnitude forces are applied to a door at the doorknob.The first force is applied perpendicular to the door,and the second force is applied at 30° to the plane of the door.Which force exerts the greater torque about the door hinge?

Accepted Answer

The torque exerted by a force depends on the angle at which the force is applied. The torque is maximized when the force is applied perpendicular to the lever arm (in this case, the door), as in the first force. The second force, applied at an angle, has a component perpendicular to the door that is less than the magnitude of the first force, resulting in a smaller torque.

Question 4

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°)between the wrench handle and the direction of the applied force?

Accepted Answer

The torque is given by the formula:$$	au = Fd\sin	heta$$where:$$	au$$ is the torque in N·mF is the force in Nd is the distance from the pivot point to the point where the force is applied in m$$	heta$$ is the angle between the force and the distance vector in radiansWe can rearrange this formula to solve for $$	heta$$:$$	heta = \sin^{-1}\left(\frac{	au}{Fd}ight)$$Plugging in the given values, we get:$$	heta = \sin^{-1}\left(\frac{15	ext{ N$\cdot$m}}{(95	ext{ N})(0.32	ext{ m})}ight) = 30^\circ$$Therefore, the angle between the wrench handle and the direction of the applied force is 30°.

Question 5

When a car is weighed,it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale,and then records a second reading as the rear wheels go over the scale.The weight of the car is equal to

Accepted Answer

The weight of the car is distributed over all four wheels of the car, so the weight recorded by the front wheels and the weight recorded by the rear wheels will not be the same. Therefore, the weight of the car is the sum of the two readings recorded by the scale, which is choice D, the sum of the two weights.

Question 6

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

Accepted Answer

Torque = Force x Distance x sin(angle)= 17 N x 0.63 m x sin(45°)= 7.6 N ∙ m

Question 7

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice. )

Accepted Answer

CWhen the skater pulls in her arms, she reduces her moment of inertia and spins faster to conserve angular momentum (A), as no external torques act on her. The kinetic energy remains constant (C) because the work done is internal and does not add or remove energy from the system.

Question 8

If the sum of the external torques on an object is zero,then the sum of the external forces on it must also be zero.

Accepted Answer

The sum of the external torques being zero ensures rotational equilibrium, but the sum of the external forces can be nonzero if those forces are acting in such a way that they cancel out each other's rotational effects but still produce a net linear force on the object.

Question 9

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that

Accepted Answer

When Diego moves towards the center of the merry-go-round, his distance from the axis of rotation decreases, which reduces the moment of inertia of the system. According to the law of conservation of angular momentum, the product of moment of inertia and angular velocity must remain constant. Therefore, if the moment of inertia decreases, the angular velocity must increase to keep their product constant. Hence, the correct choice is A.

Question 10

As shown in the figure,a given force is applied to a rod in several different ways.In which case is the torque about the pivot P due to this force the greatest?

Accepted Answer

The answer of As shown in the figure,a given force...

Question 11

A croquet mallet balances when suspended from its center of mass,as shown in the left part of the figure.If you cut the mallet into two pieces at its center of mass,as shown in the right part of the figure,how do the masses of the two pieces compare? (There could be more than one correct choice. )

Accepted Answer

The answer of A croquet mallet balances when suspended from...

Question 12

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

Accepted Answer

The answer of A man in a gym is holding...

Question 13

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

Accepted Answer

When the person extends her arms, her moment of inertia increases as the mass is now distributed further away from the axis of rotation. As per the conservation of angular momentum, the angular velocity must decrease because the product of moment of inertia and angular velocity must remain constant. Therefore, the correct choice is D.

Question 14

If the sum of both the external torques and the external forces on an object is zero,then the object must be at rest.

Accepted Answer

An object can be moving at a constant velocity (not accelerating) if both the sum of external torques and external forces are zero, due to Newton's first law of motion.

Question 15

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is horizontal?

Accepted Answer

The answer of A man in a gym is holding...

Question 16

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.If a 30-cm long wrench is used,what is the magnitude of the minimum force required using the wrench?

Accepted Answer

The formula for torque is T = F x d, where T is torque, F is force, and d is the lever arm (distance from the axis of rotation to where the force is applied). Rearranging the formula to solve for force, we get F = T/d. 
Substituting the values, we get F = 90 N ∙ m / 0.3 m = 300 N. Therefore, the minimum force required using the wrench is 300 N.

Question 17

Five forces act on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice. )

Accepted Answer

The direction of torque is given by the cross product of the force and the vector from the pivot point to the point where the force is applied. Force C acts perpendicular to the vector from P to its point of application, creating a counter-clockwise torque about point P.

Question 18

When is the angular momentum of a system constant?

Accepted Answer

Angular momentum of a system is conserved (constant) only when there is no net external torque acting on the system. This is known as the law of conservation of angular momentum.

Question 19

Two forces produce equal torques on a door about the door hinge.The first force is applied at the midpoint of the door;the second force is applied at the doorknob.Both forces are applied perpendicular to the door.Which force has a greater magnitude?

Accepted Answer

Torque is the product of force and the distance from the pivot point. Since the first force is applied at the midpoint, which is closer to the hinge than the doorknob, it must have a greater magnitude to produce the same torque as the second force applied at the doorknob.

Question 20

If the answer to your calculation has units of kg ∙ m²/s,what type of quantity could it be? (There could be more than one correct choice).

Accepted Answer

Angular momentum has units of kg ∙ m²/s, which matches the given units.

Quiz 11: Rotational Dynamics and Static Equilibrium

If an object remains at rest,then the sum of both the external torques and the external forces on the object must be zero.

If the sum of the external forces on an object is zero,then the sum of the external torques on it must also be zero.

Two equal-magnitude forces are applied to a door at the doorknob.The first force is applied perpendicular to the door,and the second force is applied at 30° to the plane of the door.Which force exerts the greater torque about the door hinge?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

When a car is weighed,it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale,and then records a second reading as the rear wheels go over the scale.The weight of the car is equal to

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice. )

If the sum of the external torques on an object is zero,then the sum of the external forces on it must also be zero.

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that

As shown in the figure,a given force is applied to a rod in several different ways.In which case is the torque about the pivot P due to this force the greatest?

A croquet mallet balances when suspended from its center of mass,as shown in the left part of the figure.If you cut the mallet into two pieces at its center of mass,as shown in the right part of the figure,how do the masses of the two pieces compare? (There could be more than one correct choice. )

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

If the sum of both the external torques and the external forces on an object is zero,then the object must be at rest.

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is horizontal?

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.If a 30-cm long wrench is used,what is the magnitude of the minimum force required using the wrench?

Five forces act on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice. )

When is the angular momentum of a system constant?

Two forces produce equal torques on a door about the door hinge.The first force is applied at the midpoint of the door;the second force is applied at the doorknob.Both forces are applied perpendicular to the door.Which force has a greater magnitude?

If the answer to your calculation has units of kg ∙ m²/s,what type of quantity could it be? (There could be more than one correct choice) .

Quiz 11: Rotational Dynamics and Static Equilibrium

If an object remains at rest,then the sum of both the external torques and the external forces on the object must be zero.

If the sum of the external forces on an object is zero,then the sum of the external torques on it must also be zero.

Two equal-magnitude forces are applied to a door at the doorknob.The first force is applied perpendicular to the door,and the second force is applied at 30° to the plane of the door.Which force exerts the greater torque about the door hinge?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

When a car is weighed,it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale,and then records a second reading as the rear wheels go over the scale.The weight of the car is equal to

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice. )

If the sum of the external torques on an object is zero,then the sum of the external forces on it must also be zero.

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that

As shown in the figure,a given force is applied to a rod in several different ways.In which case is the torque about the pivot P due to this force the greatest?

A croquet mallet balances when suspended from its center of mass,as shown in the left part of the figure.If you cut the mallet into two pieces at its center of mass,as shown in the right part of the figure,how do the masses of the two pieces compare? (There could be more than one correct choice. )

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

If the sum of both the external torques and the external forces on an object is zero,then the object must be at rest.

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is horizontal?

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.If a 30-cm long wrench is used,what is the magnitude of the minimum force required using the wrench?

Five forces act on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice. )

When is the angular momentum of a system constant?

Two forces produce equal torques on a door about the door hinge.The first force is applied at the midpoint of the door;the second force is applied at the doorknob.Both forces are applied perpendicular to the door.Which force has a greater magnitude?

If the answer to your calculation has units of kg ∙ m2/s,what type of quantity could it be? (There could be more than one correct choice) .

If the answer to your calculation has units of kg ∙ m²/s,what type of quantity could it be? (There could be more than one correct choice) .