Question 1

A machinist turns on the power to a grinding wheel at time $$t = 0. $$The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of 35 rad/s. The wheel is then run at that angular velocity for 30 s, and then power is shut off. The wheel slows down uniformly at 1.4 rad/s$$^2$$ until the wheel stops. What is the total number of revolutions made by the wheel in this situation?

Accepted Answer

$$1200$$

Question 2

A pulley has an initial angular speed of $$12.5$$ rad/s and a constant angular acceleration of $$3.41$$ rad/s$$^2. $$Through what angle does the pulley turn in $$5.26 s$$?

Accepted Answer

$$113$$ rad$

Question 3

An old 78 rpm record rotates through an angle of $$120^	ext{o} as it $$slows down uniformly from $$78.0$$ rpm to $$22.5$$ rpm. What is the magnitude of the angular acceleration of the record?

Accepted Answer

$$0.324$$ rad/s$$^2$$

Question 4

A man in a gym is holding an $$8.0-kg $$weight at arm's length, a distance of $$0.55 m $$from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at $$30^	ext{o}$$ below the horizontal?

Accepted Answer

$$22 N$$ \cdot m$

Question 5

A force of $$12 N is $$applied to the end of a $$0.43-m $$long torque wrench at an angle of $$58^	ext{o}$$ from a line joining the pivot point to the handle. What is the magnitude of the torque about the pivot point produced by this force?

Accepted Answer

$$4.37 N$$ \cdot m$

Question 6

The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude $$F = 720 N. $$What is the magnitude of the torque that this force produces about the ankle joint?

Accepted Answer

$$36 N$$ \cdot m$

Question 7

A uniform solid cylinder of mass $$10 kg $$can rotate about a frictionless axle through its center $$O$$, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius $$R_1 = 1.0$ m exerts a force of magnitude F_1$ = 5.0 N to $$the right. A second rope wrapped around another section of radius $$R_2 = 0.50$ m exerts a force of magnitude F_2$ = 6.0 N $$downward. What is the angular acceleration of the cylinder?

Accepted Answer

$$0.60$$ rad/s$$^2$$

Question 8

As shown in the figure, a $$3.50-kg $$box is attached to a light string that is wrapped around a cylindrical frictionless spindle of radius $$0.10 m $$and moment of inertia $$4.00 	imes 10$$^{-3}$$ kg m^2$. The spool is suspended from the ceiling, and the box is then released from rest a distance 3.50$ m above the floor. How long does it take for the box to reach the floor?

Accepted Answer

$$2.27 s$

Question 9

Two astronauts, masses $$60 kg $$and $$80 kg$$, initially right next to each other and at rest in outer space. They suddenly push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved by $$12 m$$?

Accepted Answer

$$9 m$

Question 10

A hockey puck of mass $$0.16 kg $$and velocity of $$21 m/s is $$struck by the bat with an external force of $$500 N$$, which results in a velocity of $$37 m/s in $$the opposite direction from the original motion. The time interval the bat and ball are in contact is $$2.0 	imes 10$$^{-3}$$ s. What is the magnitude of the impulse delivered to the puck?

Accepted Answer

$$14 N$$ \cdot s$

Question 11

A batter hits a foul ball. The $$0.14-kg $$baseball that was approaching him at $$40 m/s $$leaves the bat at $$30 m/s in $$the opposite direction to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the ball?

Accepted Answer

$$9.8 N$$ \cdot s$

Rotational Motion and Torque: Multiple Choice Study Guide

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