Question 1

A box of mass $$m is $$placed on a cart of mass $$M$$ and is pushed forward by a force $$F. $$The box does not slide due to friction. Which of the following best describes the direction and type of friction acting on the box?

Accepted Answer

Upwards static friction, opposing gravity

Question 2

A mass $$m is $$spinning in a circle of radius $$R on a $$frictionless table, attached to a string that passes through a hole and suspends a mass $$3m$$ below. What is the tension $$T in $$the string when the system is in equilibrium?

Accepted Answer

$$T = 3mg$$

Question 3

Given the centripetal acceleration formula $$a_{rad} = \frac{v^2$}{R}$$, if a mass $$m is $$spinning such that the tension in the string is $$3mg$$, what is the required speed $$v of $$the mass?

Accepted Answer

$$v = \sqrt{3gR}$$

Question 4

A spaceship orbits a planet at a distance $$R$$ from its center, taking a time $$T_0 to $$complete one orbit. What is the linear speed $$v of $$the spaceship?

Accepted Answer

$$v = 2\pi R / T_0$

Question 5

Using Newton's second law for rotation, which equation correctly relates the sum of torques to angular acceleration?

Accepted Answer

$$\sum 	au = I \alpha$$

Question 6

A rod is pivoted at its center with three forces acting: $$3F_0 at $$one end, $$F_0 at $$the other, and $$F_A at a $$distance $$r at$$ $$30^\circ to $$the rod. If the net torque is zero, what is the value of $$F_A$$?

Accepted Answer

$$F_A = 4F_0$$

Question 7

Andrew stands two-thirds up a frictionless ladder of mass $$\frac{1}{2}m. A $$rope connects the bottom to the wall. What is the normal force $$N_{pg}$$ exerted by the ladder at the point where Andrew stands?

Accepted Answer

$$N_{pg} = mg$$

Question 8

For a box of mass $$m$$ hanging from a pulley of mass $$3m$$ and radius $$R$$, what is the relationship between the box's linear acceleration $$a$$ and the pulley's angular acceleration $$\alpha$$?

Accepted Answer

$$a = R\alpha$$

Question 9

A box of mass $$m is $$released and accelerates downward, causing a pulley of mass $$3m$$ and radius $$R to $$rotate. What is the box's acceleration $$a$$?

Accepted Answer

$$a = \frac{2}{5}g$$

Question 10

Which equation correctly relates the period $$T of $$circular motion to angular velocity $$\omega$$?

Accepted Answer

$$\omega = \frac{2\pi}{T}$$

Question 11

A satellite of mass $$m$$ orbits a planet of mass $$M at $$radius $$R. $$Using Newton's law of gravitation and centripetal force, what is the correct expression for the planet's mass $$M in $$terms of the satellite's period $$T_0$$?

Accepted Answer

$$M = \frac{4\pi^2$ R^3$}{G T_0$^2}$$

Question 12

Which of the following is the correct equation for momentum conservation in a collision?

Accepted Answer

$$m_1 v_i$$ = $$m_2 v_f$

Question 13

If a mass $$m is $$moving in a circle of radius $$R$$ with speed $$v$$, what is the direction of the net force acting on the mass?

Accepted Answer

Towards the center of the circle

Question 14

A pulley of mass $$3m$$ and radius $$R is $$acted on by a tension $$T at $$its edge. What is the torque $$	au$$ produced by the tension?

Accepted Answer

$$	au = R T$$

Question 15

Which of the following is the correct formula for the distance $$s$$ traveled in circular motion for an angle $$	heta (in $$radians) and radius $$R$$?

Accepted Answer

$$s = R 	heta$$

Question 16

A box is suspended by a rope and is in equilibrium. Which forces act on the box?

Accepted Answer

Gravity downward and tension upward

Question 17

In a free-body diagram, which force is always perpendicular to the surface of contact?

Accepted Answer

Normal force

Question 18

If a box is not sliding on a cart, what type of friction is present between the box and the cart?

Accepted Answer

Static friction

Question 19

Which equation correctly relates the linear velocity $$v to $$angular velocity $$\omega$$ and radius $$R$$?

Accepted Answer

$$v = R \omega$$

Fundamentals of Forces, Motion, and Rotational Dynamics: Study Notes

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