Q: A force of 10 N is applied tangentially to the rim of a wheel with a radius of 0.5 m. What is the torque produced?

$$\tau = 5\ \mathrm{N\cdot m}$$

Q: A wrench 0.3 m long is used to loosen a bolt. If a force of 40 N is applied at the end at an angle of $$90^\circ to $$the wrench, what is the torque?

$$\tau = 12\ \mathrm{N\cdot m}$$

Question 1

A 2 kg ball moving at 5 m/s collides head-on and sticks to a stationary 3 kg ball. What is the final velocity of the combined mass after the collision? (Assume a perfectly inelastic collision.)

Accepted Answer

$$v_f = 2\ \mathrm{m/s}$$

Question 2

Which of the following statements best describes the difference between elastic and inelastic collisions?

Accepted Answer

In elastic collisions, both momentum and kinetic energy are conserved; in inelastic collisions, only momentum is conserved.

Question 3

A 0.2 kg hockey puck slides on ice at 4 m/s and collides elastically with a stationary 0.3 kg puck. What is the velocity of the 0.2 kg puck after the collision?

Accepted Answer

$$v = -0.8\ \mathrm{m/s}$$

Question 4

A disk rotates from rest with a constant angular acceleration of $$2\ \mathrm{$$rad/s^2$$}. $$What is its angular velocity after 5 seconds?

Accepted Answer

$$\omega = 10\ \mathrm{rad/s}$$

Question 5

Which equation correctly relates linear velocity $$v$$ and angular velocity $$\omega$$ for a point at radius $$r$$ from the axis of rotation?

Accepted Answer

$$v = r\omega$$

Question 6

A force of 10 N is applied tangentially to the rim of a wheel with a radius of 0.5 m. What is the torque produced?

Accepted Answer

$$	au = 5\ \mathrm{N\cdot m}$$

Question 7

A uniform rod of length 2 m and mass 3 kg is pivoted at one end. What is its moment of inertia about the pivot?

Accepted Answer

$$I = 4\ \mathrm{kg\cdot m^2$}$$

Question 8

A car of mass 1000 kg moving at 20 m/s crashes into a wall and comes to rest in 0.1 s. What is the average force exerted by the wall on the car?

Accepted Answer

$$F = -200,000\ \mathrm{N}$$

Question 9

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

Accepted Answer

Torque is the rotational equivalent of force, causing angular acceleration.

Question 10

A spinning figure skater pulls in her arms, reducing her moment of inertia to half. If her initial angular velocity was $$\$$omega_0$$, what is her final angular velocity?

Accepted Answer

$$2\$$omega_0$$

Question 11

A solid sphere and a hollow sphere of equal mass and radius roll down an incline without slipping. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 12

A 0.5 kg ball moving at 6 m/s collides elastically with a 1 kg ball at rest. What is the velocity of the 1 kg ball after the collision?

Accepted Answer

$$v = 4\ \mathrm{m/s}$$

Question 13

Which of the following equations correctly expresses Newton's second law for rotation?

Accepted Answer

$$	au = I\alpha$$

Question 14

A rotating platform speeds up from 2 rad/s to 8 rad/s in 3 seconds. What is its angular acceleration?

Accepted Answer

$$\alpha = 2\ \mathrm{$$rad/s^2$$}$$

Question 15

A 2 kg object moves in a circle of radius 0.5 m at a constant speed of 4 m/s. What is its angular momentum about the center?

Accepted Answer

$$L = 4\ \mathrm{kg\cdot m^2$/s}$$

Question 16

A 0.1 kg bullet is fired at 300 m/s into a 2 kg wooden block at rest on a frictionless surface. The bullet embeds in the block. What is the final velocity of the block-bullet system?

Accepted Answer

$$v_f = 14.3\ \mathrm{m/s}$$

Question 17

Which of the following is NOT a valid connection between linear and rotational quantities?

Accepted Answer

$$F = m\alpha$$

Question 18

A wrench 0.3 m long is used to loosen a bolt. If a force of 40 N is applied at the end at an angle of $$90^\circ to $$the wrench, what is the torque?

Accepted Answer

$$	au = 12\ \mathrm{N\cdot m}$$

Question 19

A child sits on a merry-go-round at a distance of 2 m from the center, which rotates at 0.5 rad/s. What is the child's linear speed?

Accepted Answer

$$v = 1\ \mathrm{m/s}$$

Question 20

A 5 kg object is subjected to a net torque of $$15\ \mathrm{N\cdot m}$$, and its moment of inertia is $$3\ \mathrm{kg\cdot m^2$}. $$What is its angular acceleration?

Accepted Answer

$$\alpha = 5\ \mathrm{$$rad/s^2$$}$$

Linear Momentum, Collisions, and Rotational Dynamics: Study Notes

스터디 가이드 - 연습 문제

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