Q: A plumber stands on the end of a wrench handle, applying a force of $$900\ \text{N} at a $$distance of $$0.80\ \text{m}$$ from the pivot, at an angle of $$19^\circ to $$the horizontal. What is the magnitude of the torque?

$$\tau = 900 \times 0.80 \times \sin(19^\circ)$$

Q: A uniform ladder of length $$L$$ and weight $$W$$ leans against a frictionless wall at angle $$\theta. A $$person of weight $$W_p$$ stands a distance $$d up $$the ladder. What is the minimum coefficient of static friction $$\mu_s$$ required at the base to prevent slipping?

$$\mu_s = \frac{(W_p d + W \frac{L}{2}) \cos \theta}{(W_p + W) \sin \theta}$$

Q: A rigid body is in equilibrium. Which conditions must be satisfied?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Q: A merry-go-round platform of radius $$R is $$acted upon by a tangential force $$F_{tan}$$ for an angular displacement $$\Delta \theta. $$What is the work done?

$$W = F_{tan} R \Delta \theta$$

Question 1

A cyclist accelerates from rest, causing the wheels to rotate. If the radius of the wheel is $$r$$ and the angular acceleration is $$\alpha$$, what is the linear acceleration $$a of a $$point on the rim?

Accepted Answer

$$a = r \alpha$$

Question 2

A solid disk of mass $$M$$ and radius $$R is $$rolling without slipping down an incline. What is the relationship between its translational velocity $$v_{CM}$$ and its angular velocity $$\omega$$?

Accepted Answer

$$v_{CM} = R \omega$$

Question 3

A wrench is used to loosen a bolt. Which of the following actions will maximize the torque applied to the bolt?

Accepted Answer

Applying the force perpendicular to the wrench at the farthest point from the bolt

Question 4

A plumber stands on the end of a wrench handle, applying a force of $$900\ 	ext{N} at a $$distance of $$0.80\ 	ext{m}$$ from the pivot, at an angle of $$19^\circ to $$the horizontal. What is the magnitude of the torque?

Accepted Answer

$$	au = 900 	imes 0.80 	imes \sin(19^\circ)$$

Question 5

A uniform ladder of length $$L$$ and weight $$W$$ leans against a frictionless wall at angle $$	heta. A $$person of weight $$W_p$$ stands a distance $$d up $$the ladder. What is the minimum coefficient of static friction $$\mu_s$$ required at the base to prevent slipping?

Accepted Answer

$$\mu_s = \frac{(W_p d + W \frac{L}{2}) \cos 	heta}{(W_p + W) \sin 	heta}$$

Question 6

A spinning ice skater pulls her arms in, 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 7

A block slides in a circular path on a frictionless plane. The radius is reduced to half its original value by pulling the string. If the initial speed is $$v_i$$, what is the new speed?

Accepted Answer

$$2 v_i$$

Question 8

A cable is wrapped around a uniform solid cylinder of mass $$M$$ and radius $$R. If a $$force $$F is $$applied to the cable, what is the angular acceleration $$\alpha of $$the cylinder?

Accepted Answer

$$\alpha = \frac{F R}{\frac{1}{2} M R^2$}$$

Question 9

Two disks, with moments of inertia $$I_A$$ and $$I_B$$, rotate with angular velocities $$\omega_A$$ and $$\omega_B. $$They are pushed together and reach a common angular velocity $$\omega_f. $$What is $$\omega_f$$?

Accepted Answer

$$\omega_f = \frac{I_A \omega_A + I_B \omega_B}{I_A + I_B}$$

Question 10

A rigid body is in equilibrium. Which conditions must be satisfied?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Question 11

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$\phi$$ with the moment arm. What is the torque $$	au$$?

Accepted Answer

$$	au = F r \sin \phi$$

Question 12

Which of the following statements about angular momentum is correct?

Accepted Answer

Angular momentum is conserved when the net external torque is zero.

Question 13

A solid sphere and a hollow sphere of equal mass and radius roll down the same incline. Which reaches the bottom first?

Accepted Answer

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

Question 14

A merry-go-round platform of radius $$R is $$acted upon by a tangential force $$F_{tan}$$ for an angular displacement $$\Delta 	heta. $$What is the work done?

Accepted Answer

$$W = F_{tan} R \Delta 	heta$$

Question 15

A rotating rigid body has moment of inertia $$I$$ and angular velocity $$\omega. $$What is its angular momentum $$L$$?

Accepted Answer

$$L = I \omega$$

Question 16

A torque $$	au$$ acts on a rotating body for a time $$\Delta t. $$What is the change in angular momentum $$\Delta L$$?

Accepted Answer

$$\Delta L = 	au \Delta t$$

Question 17

A solid cylinder, a hollow cylinder, and a thin-walled hollow cylinder all have the same mass and radius. A force $$F is $$applied at the outer radius for the first two and at the inner radius for the third. Which ranks their angular accelerations from smallest to largest?

Accepted Answer

$$\$$alpha_3$$ \u003e \$$alpha_2$$ \u003e \$$alpha_1$$

Question 18

A physics professor stands on a turntable holding dumbbells. If he pulls the dumbbells inward, what happens to his angular velocity and kinetic energy?

Accepted Answer

Angular velocity increases, and kinetic energy increases.

Question 19

Which force applied to a door will be most effective in opening it?

Accepted Answer

A force applied perpendicular to the door at the farthest point from the hinge.

Dynamics of Rotational Motion: Chapter 10 Study Notes

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