Q: A 2 kg object is lifted to a height of 5 m. What is its gravitational potential energy at that height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$PE = 2 \times 9.8 \times 5 = 98\ \mathrm{J}$$

Question 1

Which of the following best describes the work-energy theorem?

Accepted Answer

The work done on an object is equal to the change in its kinetic energy: $$W = \Delta KE$$

Question 2

A 2 kg object is lifted to a height of 5 m. What is its gravitational potential energy at that height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$PE = 2 	imes 9.8 	imes 5 = 98\ \mathrm{J}$$

Question 3

Which of the following statements about rotational inertia is correct?

Accepted Answer

Rotational inertia is greater when most of the mass is located far from the axis of rotation.

Question 4

A hoop and a solid disk of equal 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 a smaller rotational inertia.

Question 5

Which equation correctly relates tangential speed $$v$$, angular speed $$\omega$$, and radius $$r$$ for a point on a rotating object?

Accepted Answer

$$v = r \omega$$

Question 6

A person is spinning on a rotating stool with arms extended holding weights. What happens to their rotational speed if they pull the weights inward, and why?

Accepted Answer

Their rotational speed increases because their rotational inertia decreases, conserving angular momentum.

Question 7

Which of the following best defines torque?

Accepted Answer

Torque is the product of the lever arm and the force applied perpendicular to it: $$	au = rF$$

Question 8

A seesaw is balanced even though one child is heavier than the other. What must be true for the seesaw to be in equilibrium?

Accepted Answer

The product of each child's weight and their distance from the pivot must be equal: $$m_1$$ $$r_1$$ = $$m_2$$ $$r_2$$

Question 9

Which of the following is true about the center of mass of an object?

Accepted Answer

It is the point that moves as if all the mass of the system were concentrated there.

Question 10

A ball is thrown and follows a parabolic trajectory. Which point on the ball follows this path?

Accepted Answer

The center of mass of the ball.

Question 11

Which of the following is the correct formula for the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$d$$?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{d^2$}$$

Question 12

If the distance between two objects is doubled, what happens to the gravitational force between them?

Accepted Answer

It becomes one-fourth as large.

Question 13

Which of the following best describes centripetal force?

Accepted Answer

It is the force directed toward the center of a circle that keeps an object moving in a circular path.

Question 14

A car of mass $$m$$ moves at tangential speed $$v$$ around a curve of radius $$r. $$What is the required centripetal force?

Accepted Answer

$$F = \frac{mv^2$}{r}$$

Question 15

Which of the following is the correct expression for angular momentum $$L of a $$rotating object?

Accepted Answer

$$L = I \omega$$

Question 16

A satellite orbits Earth at a height $$h$$ above the surface. What is the correct formula for the acceleration due to gravity at that height?

Accepted Answer

$$g(h) = G \frac{M_e}{(R_e + h)^2$}$$

Question 17

Which of the following statements about the law of conservation of angular momentum is correct?

Accepted Answer

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

Question 18

A door is easiest to open when you push:

Accepted Answer

At the edge farthest from the hinges, perpendicular to the door.

Question 19

Which of the following is true about the center of gravity and stability of an object?

Accepted Answer

An object is stable if a vertical line from its center of gravity falls within its base.

module 5 lecture 9: Rotational Motion, Torque, and Gravitation

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