Question 1

A windmill with a radius of 25 m spins with a linear velocity of 6.3 m/s. What is its angular velocity in $$\mathrm{rad/s}$$?

Accepted Answer

$$0.252\ \mathrm{rad/s}$$

Question 2

If the windmill's linear velocity decreases from $$6.3\ \mathrm{m/s} to$$ $$2.6\ \mathrm{m/s} in$$ $$10\ \mathrm{s}$$, what is the average angular acceleration?

Accepted Answer

$$-0.0148\ \mathrm{$$rad/s^2$$}$$

Question 3

Given the angular acceleration from the previous question, what is the windmill's angular velocity after $$123\ \mathrm{s}$$, starting from $$0.252\ \mathrm{rad/s}$$?

Accepted Answer

$$-1.5684\ \mathrm{rad/s}$$

Question 4

A bowling ball with a diameter of $$20\ \mathrm{cm} is $$rolled at $$17\ \mathrm{mph}$$ and has $$202.143\ \mathrm{J} of $$kinetic energy. What is the mass of the ball?

Accepted Answer

$$5\ \mathrm{kg}$$

Question 5

If the mass of the bowling ball is doubled, what is the new kinetic energy?

Accepted Answer

$$404.286\ \mathrm{J}$$

Question 6

A student lies on a plank supported by two scales $$2.50\ \mathrm{m}$$ apart. The left scale reads $$300\ \mathrm{N}$$ and the right reads $$122\ \mathrm{N}. $$What is the student's mass?

Accepted Answer

$$43.1\ \mathrm{kg}$$

Question 7

Using the same scenario, what is the distance from the student's head to her center of mass?

Accepted Answer

$$0.723\ \mathrm{m}$$

Question 8

If the left support is removed and the student is treated as a long thin rod, what is the angular acceleration about the right support?

Accepted Answer

$$8.326\ \mathrm{$$rad/s^2$$}$$

Question 9

A ship of mass $$3 	imes 10^8$\ \mathrm{kg} is$$ $$15$$ miles from the centerline between two asteroids ($$M_1 = 1.5$$ 	imes $$10^{10}$$\ \mathrm{kg}$$, M_2$ = 3.0 	imes 10$$^{10}$$\ \mathrm{kg}) $$separated by $$16$$ miles. What is the $$x-$$component of the gravitational force from $$M_1 on $$the ship?

Accepted Answer

$$0.353$$

Question 10

What is the total gravitational force vector (in terms of $$x$$ and $$y$$ components) acting on the ship from both asteroids?

Accepted Answer

$$F_G = 1.059x - 0.188y$$

Question 11

Which equation correctly relates the linear velocity $$v$$ and angular velocity $$\omega$$ for a rotating object of radius $$r$$?

Accepted Answer

$$\omega = \frac{v}{r}$$

Question 12

For a solid sphere, what is the correct expression for its moment of inertia about its center?

Accepted Answer

$$I = \frac{2}{5}mr^2$

Question 13

A windmill slows down with a constant angular acceleration. Which kinematic equation would you use to find its angular velocity after a certain time?

Accepted Answer

$$\omega_f = \omega_i + \alpha t$$

Question 14

A plank is supported at both ends with a student lying on it. If the left scale reads higher than the right, where is the student's center of mass relative to the plank?

Accepted Answer

Closer to the left end

Question 15

If the gravitational force between two masses is $$F = G\frac{m_1$ m_2$}{r^2$}$$, what happens to the force if the distance between them is doubled?

Accepted Answer

It becomes one-fourth as large

Question 16

A bowling ball's kinetic energy is given by $$KE = \frac{1}{2}mv^2$ + \frac{1}{2}I\$$omega^2$$. If the ball rolls without slipping, which relationship holds between v$ and $$\omega$$?

Accepted Answer

$$v = \omega r$$

Question 17

A student is modeled as a uniform rod of length $$2.5\ \mathrm{m}$$ and mass $$43.1\ \mathrm{kg}. $$What is the moment of inertia about one end?

Accepted Answer

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

Question 18

If a force is applied at a distance $$r$$ from the axis of rotation, what is the torque produced?

Accepted Answer

$$	au = rF$$

Question 19

A ship is affected by two gravitational forces at angles $$\pm 28.07^\circ$$ from the $$x-$$axis. If the $$y-$$components are $$0.188$$ and $$-0.376$$, what is the net $$y-$$component?

Accepted Answer

$$-0.188$$

Physics Rotational Motion, Energy, Center of Mass, and Gravitation Study Guide

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