Q: Which of the following is the correct expression for the torque $$\tau$$ produced by a force $$\vec{F}$$ applied at a position vector $$\vec{r}$$ from the axis of rotation?

$$\tau = \vec{r} \times \vec{F}$$

Question 1

Which of the following best describes the condition for static equilibrium in a rigid body?

Accepted Answer

The net force and net torque on the body must both be zero.

Question 2

A uniform beam of length $$L$$ and mass $$m is $$supported horizontally at its ends. A mass $$M is $$hung at a distance $$d$$ from the left end. What is the upward force exerted by the left support?

Accepted Answer

$$\frac{m g}{2} + \frac{M g (L-d)}{L}$$

Question 3

Given a graph of angular velocity $$\omega$$ versus time $$t$$ for a rotating object, how can you determine the angular displacement $$	heta$$ over a time interval?

Accepted Answer

By calculating the area under the $$\omega vs$$. $$t$$ curve for that interval.

Question 4

A disk of mass $$m$$ and radius $$R$$ rotates about its center with angular velocity $$\omega. $$What is its angular momentum?

Accepted Answer

$$\frac{1}{2} m R^2$ \omega$$

Question 5

A figure skater pulls in her arms while spinning, reducing her moment of inertia from $$I_1 to$$ $$I_2. If $$her initial angular velocity is $$\$$omega_1$$, what is her final angular velocity $$\$$omega_2$$?

Accepted Answer

$$\$$omega_2$$ = \frac{I_1$}{I_2$} \$$omega_1$$

Question 6

Which of the following is the correct expression for the torque $$	au$$ produced by a force $$\vec{F}$$ applied at a position vector $$\vec{r}$$ from the axis of rotation?

Accepted Answer

$$	au = \vec{r} 	imes \vec{F}$$

Question 7

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 8

A wheel of radius $$R$$ rotates with constant angular acceleration $$\alpha. If it $$starts from rest, what is its angular velocity $$\omega$$ after time $$t$$?

Accepted Answer

$$\omega = \alpha t$$

Question 9

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

Accepted Answer

$$v = r \omega$$

Question 10

A force $$F is $$applied tangentially to the rim of a wheel of radius $$R$$ and moment of inertia $$I. $$What is the resulting angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{F R}{I}$$

Question 11

A rotating object has a constant angular velocity $$\omega. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = 0$$

Question 12

A rod of length $$L$$ and mass $$m$$ rotates about one end. What is its moment of inertia?

Accepted Answer

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

Question 13

A car's wheels lock and it skids to a stop. Which principle explains why the car's angular momentum is not conserved?

Accepted Answer

An external torque acts on the wheels due to friction with the road.

Question 14

A satellite orbits Earth in a circular path. If no external torque acts, what happens to its angular momentum?

Accepted Answer

It remains constant.

Question 15

A door of width $$w is $$pushed with force $$F at $$its edge, perpendicular to the surface. What is the torque about the hinges?

Accepted Answer

$$	au = F w$$

Question 16

A spinning neutron star contracts, reducing its radius by half. Assuming mass remains constant, by what factor does its angular velocity change?

Accepted Answer

It increases by a factor of 4.

Question 17

A rotating object slows down due to friction. Which of the following best describes the effect of friction?

Accepted Answer

Friction exerts an external torque, reducing angular velocity.

Question 18

A gymnast jumps and tucks her body to spin faster. Which law explains this change?

Accepted Answer

Conservation of angular momentum.

Question 19

A rotating platform has a moment of inertia $$I$$ and angular velocity $$\omega. If a $$person of mass $$m$$ stands at a distance $$r$$ from the center, what is the new moment of inertia?

Accepted Answer

$$I_{new} = I + m r^2$

Question 20

A bicycle wheel spins freely. If you touch the rim lightly, what happens to its angular velocity and why?

Accepted Answer

It decreases due to an external torque from friction.

Equilibrium, Rotational Kinematics, and Dynamics: Study Guide Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드