Q: A wrench is 0.3 m long. If a force of 20 N is applied perpendicular to the end of the wrench, what is the torque produced?

$$\tau = 6 \ \mathrm{N \cdot m}$$

Question 1

A disk and a hoop, both with the same mass and radius, are released from rest at the top of an incline. Which one reaches the bottom first, and why?

Accepted Answer

The disk, because it has less rotational inertia.

Question 2

A wrench is used to loosen a bolt. Which of the following actions will produce the greatest torque?

Accepted Answer

Applying a force perpendicular to the wrench at its end.

Question 3

A tightrope walker uses a long pole for balance. What is the main physical principle that explains why the pole helps with stability?

Accepted Answer

The pole increases the walker's rotational inertia.

Question 4

A car rounds a curve of radius $$r at a $$tangential speed $$v. $$What is the equation for the required centripetal force?

Accepted Answer

$$F_c = m v^2$ / r$$

Question 5

If you double the speed at which you round a bend in the road, by what factor must the centripetal force increase to prevent skidding?

Accepted Answer

It must increase by a factor of four.

Question 6

Which of the following best describes the difference between tangential speed and rotational speed for a rotating disk?

Accepted Answer

Tangential speed varies with radius, while rotational speed is the same for all points.

Question 7

A solid cylinder and a solid sphere, both with the same mass and radius, are released from rest at the top of an incline. Which one reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller rotational inertia relative to its mass.

Question 8

Which of the following statements about centrifugal force is correct?

Accepted Answer

Centrifugal force is an apparent force experienced in a rotating reference frame.

Question 9

A pencil is rotated about three different axes: through its center, through its end, and about its length. Which axis results in the greatest rotational inertia?

Accepted Answer

About the end, perpendicular to its length.

Question 10

A merry-go-round rotates at a constant angular speed $$\omega. A $$child sits at a distance $$r$$ from the center. What is the child's tangential speed?

Accepted Answer

$$v = r \omega$$

Question 11

A wrench is 0.3 m long. If a force of 20 N is applied perpendicular to the end of the wrench, what is the torque produced?

Accepted Answer

$$	au = 6 \ \mathrm{N \cdot m}$$

Question 12

A stick of length $$L$$ and mass $$m is $$rotated about one end. What is its rotational inertia?

Accepted Answer

$$I = \frac{1}{3} m L^2$

Question 13

A car of mass $$m$$ travels around a curve of radius $$r at $$speed $$v. If $$the radius is halved but the speed remains the same, how does the required centripetal force change?

Accepted Answer

It doubles.

Question 14

Which of the following best describes the center of gravity of an object?

Accepted Answer

It is the average position of the weight distribution of the object.

Question 15

A child swings a ball in a horizontal circle on a string. If the string breaks, what path does the ball follow?

Accepted Answer

It moves in a straight line tangent to the circle at the point of release.

Question 16

Which of the following increases the stability of an object?

Accepted Answer

Lowering the center of gravity and widening the base.

Question 17

A hoop and a solid cylinder have the same mass and radius. Which has the greater rotational inertia about its central axis?

Accepted Answer

The hoop.

Question 18

Which of the following is NOT a factor that affects the torque produced by a force?

Accepted Answer

The mass of the object.

Question 19

A solid sphere of mass $$m$$ and radius $$r$$ rotates about its center. What is its rotational inertia?

Accepted Answer

$$I = \frac{2}{5} m r^2$

Rotational Motion: Physics with Calculus Study Notes

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