Question 1

Which of the following statements best describes the physical meaning of torque?

Accepted Answer

Torque is the influence that changes the rotational speed of an object by acting at a distance from the axis of rotation.

Question 2

A mechanic is trying to loosen a stuck bolt using a wrench. Which of the following will produce the greatest torque?

Accepted Answer

Applying the same force farther from the axis of rotation and perpendicular to the wrench.

Question 3

Which equation correctly expresses the magnitude of torque $$	au$$ produced by a force $$F$$ applied at a distance $$r$$ from the axis of rotation at an angle $$	heta to $$the lever arm?

Accepted Answer

$$	au = rF\sin	heta$$

Question 4

What are the SI units of torque?

Accepted Answer

N$$\cdotm$$

Question 5

A force of 20 N is applied perpendicular to a wrench at a distance of 0.3 m from the axis of rotation. What is the resulting torque?

Accepted Answer

$$6 N$\cdotm$$

Question 6

If the same force is applied at different angles to the lever arm, which angle produces the maximum torque?

Accepted Answer

$$90^\circ$$

Question 7

A solid cylinder of mass $$m$$ and radius $$R is $$used as a winch to lift a bucket of mass $$m. If $$the tension in the rope is $$T$$, which equation relates the angular acceleration $$\alpha of $$the cylinder to the torque produced by the tension?

Accepted Answer

$$TR = I\alpha$$

Question 8

Which of the following factors does NOT affect the magnitude of torque produced by a force?

Accepted Answer

The mass of the object (if force and position are unchanged)

Question 9

A force $$F is $$applied at a distance $$r$$ from the axis of rotation at an angle $$	heta to $$the lever arm. Which of the following expressions gives the moment arm $$l$$?

Accepted Answer

$$l = r\sin	heta$$

Question 10

Three identical cylinders are free to rotate about an axis through their origin. A force $$F is $$applied to each at different points. Which cylinder will have the lowest angular acceleration?

Accepted Answer

The cylinder with the largest moment of inertia

Question 11

A rolling object has its axis of rotation passing through its center of mass. Which condition must be met to use the standard torque equations for analysis?

Accepted Answer

The axis of rotation must not change direction

Question 12

A force of 10 N is applied at an angle of $$60^\circ to a $$lever arm 0.5 m from the axis of rotation. What is the magnitude of the torque produced?

Accepted Answer

$$4.33 N$\cdotm$$

Question 13

Which of the following best explains why a longer wrench is more effective at loosening a stuck bolt?

Accepted Answer

A longer wrench increases the lever arm, resulting in greater torque for the same applied force.

Question 14

If no external torque acts on a rotating object, what happens to its angular acceleration?

Accepted Answer

It remains zero.

Question 15

A bucket of mass $$m$$ hangs from a winch (solid cylinder) of mass $$m$$ and radius $$R. $$What is the acceleration $$a of $$the bucket as it descends, assuming the rope does not slip?

Accepted Answer

$$a = \dfrac{2}{3}g$$

Question 16

Which of the following is true about the direction of the force for maximum torque?

Accepted Answer

The force should be applied perpendicular to the lever arm.

Question 17

A force $$F is $$applied at a point on a lever arm at a distance $$r$$ from the axis of rotation. If the force is not perpendicular to the lever arm, how do you calculate the effective torque?

Accepted Answer

$$	au = rF\sin	heta$$

Question 18

In a real-world scenario, such as opening a heavy door, which action will increase the torque applied to the door?

Accepted Answer

Pushing farther from the hinges with the same force.

Question 19

Which of the following is the correct definition of the moment arm?

Accepted Answer

The shortest distance between the force vector and the axis of rotation.

Dynamics of Rotational Motion: Torque and Its Effects

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