Question 1

A point on the edge of a rotating disk travels a greater distance in the same amount of time compared to a point near the center. What is the relationship between tangential speed ($$v$$), rotational speed ($$\omega$$), and radial distance ($$r$$)?

Accepted Answer

$$v = r \omega$$

Question 2

Which of the following best explains why a tightrope walker uses a long pole for balance?

Accepted Answer

The pole increases the walker's rotational inertia, making it harder to rotate.

Question 3

A wrench is used to loosen a bolt. Which scenario produces the greatest torque?

Accepted Answer

Applying a force perpendicular to the wrench at the end of the handle.

Question 4

A solid sphere and a solid cylinder of equal mass and radius are rolled down an incline. Which will reach the bottom first, and why?

Accepted Answer

The solid sphere, because it has lower rotational inertia.

Question 5

Which equation correctly represents the torque ($$	au) $$produced by a force ($$F) $$applied at a distance ($$r) $$from the axis of rotation?

Accepted Answer

$$	au = r 	imes F$$

Question 6

The center of gravity of an object is important for stability. Which statement is correct regarding stable equilibrium?

Accepted Answer

The line drawn straight down from the center of gravity falls inside the base of the object.

Question 7

A car rounds a curve on a wet road and skids off. Which force was insufficient to keep the car moving along the curve?

Accepted Answer

Centripetal force

Question 8

Which of the following is a common misconception about centrifugal force?

Accepted Answer

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

Question 9

A space station is designed to simulate gravity by spinning. If the radius is 1 km and it rotates at 1 revolution per minute, what is the purpose of this design?

Accepted Answer

To create a centrifugal force that simulates Earth's gravity.

Question 10

Which formula represents the angular momentum ($$L) of a $$rotating object with rotational inertia ($$I) $$and angular velocity ($$\omega$$)?

Accepted Answer

$$L = I \omega$$

Question 11

A figure skater pulls her arms inward while spinning. What happens to her rotational speed and why?

Accepted Answer

Her rotational speed increases because her rotational inertia decreases.

Question 12

Which equation gives the centripetal force ($$F_c) $$required to keep an object of mass ($$m) $$moving at tangential speed ($$v) in a $$circle of radius ($$r$$)?

Accepted Answer

$$F_c = \frac{m v^2$}{r}$$

Question 13

Which of the following best describes the law of conservation of angular momentum?

Accepted Answer

If no external net torque acts on a rotating system, its angular momentum remains constant.

Question 14

A stick is rotated about its center of gravity (CG) and about one end. Which rotation is easier and why?

Accepted Answer

About the CG, because rotational inertia is lower.

Question 15

A ball is whirled in a circle at the end of a string. If the string breaks, what path does the ball follow?

Accepted Answer

It moves in a straight line tangent to the circle.

Question 16

Which factor does NOT affect the rotational inertia of an object?

Accepted Answer

The object's color.

Question 17

A hoop and a solid sphere of equal mass and radius are spun about their normal axes. Which has greater rotational inertia?

Accepted Answer

The hoop, because its mass is farther from the axis.

Question 18

Which of the following is true about rotational speed ($$\omega) $$for points on a rigid rotating disk?

Accepted Answer

All points have the same rotational speed.

Question 19

A space station simulates gravity by spinning. If the tangential speed at the rim is increased, what happens to the simulated gravity?

Accepted Answer

Simulated gravity increases because centripetal force increases.

Rotational Motion: Concepts and Applications

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