Q: A disk rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angle $$\theta$$ in time t$, which equation describes its angular displacement?

$$\theta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 1

A bicycle wheel of radius $$0.35\ \mathrm{m}$$ accelerates uniformly from rest to an angular velocity of $$12\ \mathrm{rad/s} in$$ $$4.0\ \mathrm{s}. $$What is the angular acceleration of the wheel?

Accepted Answer

$$3.0\ \mathrm{$$rad/s^2$$}$$

Question 2

Which of the following correctly expresses the relationship between the tangential speed $$v of a $$point on a rotating object and its angular velocity $$\omega$$?

Accepted Answer

$$v = r \omega$$

Question 3

A disk rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angle $$	heta$$ in time t$, which equation describes its angular displacement?

Accepted Answer

$$	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 4

A car tire of diameter $$0.80\ \mathrm{m}$$ slows down uniformly from $$95\ \mathrm{km/h} to $$rest in $$65$$ revolutions. What is the angular acceleration of the tire?

Accepted Answer

$$-0.48\ \mathrm{$$rad/s^2$$}$$

Question 5

Which statement about torque is correct?

Accepted Answer

Torque is the product of force and the perpendicular distance from the axis of rotation.

Question 6

A uniform beam of length $$20.0\ \mathrm{m}$$ and mass $$1500\ \mathrm{kg}$$ supports a $$15,000\ \mathrm{N}$$ printing press $$5.0\ \mathrm{m}$$ from the right support column. What is the force on the left support column?

Accepted Answer

$$17,500\ \mathrm{N}$$

Question 7

A seesaw is balanced with a $$50\ \mathrm{kg}$$ boy on one end and a $$35\ \mathrm{kg}$$ girl on the other. Where should a $$25\ \mathrm{kg}$$ girl sit to balance the seesaw if the board is $$3.6\ \mathrm{m}$$ long?

Accepted Answer

At $$1.26\ \mathrm{m}$$ from the center, same side as the $$35\ \mathrm{kg}$$ girl

Question 8

Which of the following is the correct condition for equilibrium in terms of forces?

Accepted Answer

$$\sum F = 0$$

Question 9

A ladder of mass $$30\ \mathrm{kg}$$ and length $$12\ \mathrm{m}$$ leans against a smooth wall at an angle of $$60^\circ$$ with the ground. If a $$45\ \mathrm{kg}$$ person climbs the ladder, what is the maximum distance up the ladder the person can go before it slips, given the coefficient of static friction at the base is $$0.40$$?

Accepted Answer

$$6.7\ \mathrm{m}$$

Question 10

Which equation gives the rotational kinetic energy of a rotating rigid body?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 11

A uniform table of mass $$M$$ and length $$L is $$supported by two legs located $$\frac{1}{8}L$$ from each end. What is the minimum force needed at one end to tip the table?

Accepted Answer

$$F = \frac{Mg}{4}$$

Question 12

Which of the following best describes the vector nature of angular velocity?

Accepted Answer

It points along the axis of rotation, direction given by the right-hand rule.

Question 13

A rotating object has an angular velocity $$\omega$$ and angular acceleration $$\alpha. $$What is the tangential acceleration $$a_t of a $$point at a distance $$r$$ from the axis?

Accepted Answer

$$a_t = r \alpha$$

Question 14

If a wheel is rolling without slipping, what is the relationship between the linear speed $$v of $$the center of mass and the angular speed $$\omega$$?

Accepted Answer

$$v = r \omega$$

Question 15

Which of the following is the correct expression for the period $$T of a $$rotating object in terms of its frequency $$f$$?

Accepted Answer

$$T = 1 / f$$

Question 16

A $$3\ \mathrm{m}$$ long uniform beam of mass $$30\ \mathrm{kg} is $$mounted horizontally to a wall by a hinge. A cable makes an angle of $$45^\circ$$ with the beam and supports a $$37\ \mathrm{kg}$$ sign at the end. What is the tension in the cable?

Accepted Answer

$$720\ \mathrm{N}$$

Question 17

Which of the following is NOT a correct step in solving statics problems?

Accepted Answer

Ignore the direction of forces when drawing the free-body diagram.

Question 18

Which of the following is the correct formula for angular acceleration $$\alpha in $$terms of change in angular velocity $$\Delta \omega$$ and time $$\Delta t$$?

Accepted Answer

$$\alpha = \frac{\Delta \omega}{\Delta t}$$

Question 19

A force $$F is $$applied at a distance $$r$$ from the axis of rotation at an angle $$	heta to $$the lever arm. What is the magnitude of the torque $$	au$$ produced?

Accepted Answer

$$	au = F r \sin 	heta$$

Rotational Motion: Angular Quantities, Torque, and Equilibrium (Chapters 8 & 9 Study Notes)

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