Question 1

A 0.3 kg ball with an initial velocity of $$\vec{v}_i = 3\hat{i} m/s $$collides with a wall and rebounds with a velocity of $$\vec{v}_f = -4\hat{i} m/s. $$What is the impulse exerted on the ball by the wall?

Accepted Answer

$$2.1 kg$$\cdot m/s

Question 2

An 80-g particle moving with an initial speed of 50 m/s in the positive x direction strikes and sticks to a 60-g particle moving 50 m/s in the positive y direction. What is the magnitude of the velocity of the composite system after the collision?

Accepted Answer

$$31 m/s$$

Question 3

A merry-go-round rotates from rest with an angular acceleration of $$1.56$$ rad/s$$^2. $$How long does it take to rotate through the first 2 rev?

Accepted Answer

$$1.81 s$$

Question 4

A wheel, with radius $$R = 45 cm$$, initially has an angular velocity of $$2.5$$ rev/s, and is slowing down at a rate of $$2$$ rad/s$$^2. By $$the time it stops spinning about its center, what distance will a point on the outer rim have traveled?

Accepted Answer

$$4.1 m$$

Question 5

A solid ball of mass $$42.0 kg $$rolls without slipping down an incline that makes an angle of $$37^{\circ}$$ with the horizontal. If it starts from rest, what is its kinetic energy at the bottom of the incline after descending $$7.0 m$$?

Accepted Answer

$$2000 J$$

Question 6

A basketball is rolling without slipping along a horizontal surface with total kinetic energy $$20 J. $$How much of this energy is due to rotation about the center of mass? Basketballs are hollow shells: $$I = 2/3 m r^2$.

Accepted Answer

$$8.57 J$$

Question 7

A hollow, spherical shell with mass $$2.10 kg $$rolls without slipping down a $$35.0^{\circ}$$ slope. Find the acceleration, the friction force, and the minimum coefficient of static friction needed to prevent slipping.

Accepted Answer

$$3.42 m/s$^2$$, $$0.83 N$$, $$0.13$$

Question 8

A 10.4-kg bicycle wheel is rotating at $$60$$ rev/min. It is essentially a thin hoop with a radius of $$0.45$$ meters and a rotational inertia $$I = m r^2$. How much work must be done to bring it to a stop?

Accepted Answer

$$200.0 J$$

Question 9

You throw a ball with mass of $$0.40 kg $$against a brick wall. It is moving horizontally to the left at $$10 m/s $$when it hits the wall; it rebounds horizontally to the right at $$20 m/s. $$Find the impulse of the net external force on the ball during its collision with the wall.

Accepted Answer

$$4 N$$\cdot s$

Question 10

In the previous problem, if the ball is in contact with the wall for $$0.010 s$$, find the average horizontal force that the wall exerts on the ball during the impact.

Accepted Answer

$$240 N$$

Question 11

Two small spheres, each with mass $$0.0200 kg$$, are connected by a light $$1.00 m $$long rod. The spheres rotate about an axis that is perpendicular to the rod at its center. What is the angular speed in rad/s if the total kinetic energy is $$1.25 J$$?

Accepted Answer

$$25$$ rad/s

Question 12

The mass of Sun is $$2.0 	imes 10$$^{30}$$ kg and the mass of Earth is 6.0$$ 	imes $$10^{24} kg. If $$the distance between Sun and Earth is $$1.5 	imes 10$$^{11}$$ m, the center of mass of the Sun-Earth system is located at what distance from the center of the Sun (use the origin at the center of the Sun)?

Accepted Answer

$$4.5 	imes 10$$^{8}$$ m

Question 13

A playground merry-go-round has a radius of $$3.0 m $$and a rotational inertia of $$600 kg$$\cdot m$$^2. It is $$initially spinning at $$0.80$$ rad/s when a $$20 kg $$child comes from the center to the rim. When the child reaches the rim, what is the angular velocity of the merry-go-round?

Accepted Answer

$$0.67$$ rad/s

Question 14

A system consists of three particles with masses $$m_1 = 2.0$ kg, m_2$ = 1.0 kg$$, and $$m_3 = 2.0$ kg located as shown in the figure (assume m_1$ at (0,0), m_2$ at (2,0), m_3$ at (0,2)). Find the coordinates of the center of mass of the system.

Accepted Answer

$$(0.67, 0.67)$$

Question 15

One force acting on a machine part is $$\vec{F} = (-5.00\hat{i} + 4.00\hat{j}) N. $$The force acts at the point whose position vector is $$\vec{r} = (4.00\hat{i} + 3.00\hat{j}) m. $$What is the magnitude of the torque about the origin due to the force?

Accepted Answer

$$31 N$$\cdot m$

Question 16

In order to find the speed of a fast bullet, it is fired into a $$4.0 kg $$wooden block on a horizontal surface. The bullet gets stuck in the block, which starts moving with the speed of $$V = 2.3 m/s. $$Find the original speed of the bullet if its mass is $$7.54$$ grams.

Accepted Answer

$$130 m/s$$

Question 17

A 4.6 kg particle with velocity $$\vec{v} = -3\hat{i} + 5\hat{j} at$$ $$t = 30 m$$, $$y = 45 m. $$What is the angular momentum of the particle about the origin?

Accepted Answer

$$621 kg$$\cdot $$m^2/s$

Question 18

A wheel is rotating freely at angular speed $$300$$ rev/min on a shaft whose rotational inertia is negligible, and suddenly a second wheel of mass $$2.0 kg $$and radius $$0.20 m is $$dropped onto the shaft and sticks to it. What is the angular speed of the resultant combination of the shaft and two wheels?

Accepted Answer

$$93.3$$ rev/min

Question 19

At $$t = 0$$ the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by $$	heta(t) = 250$$ rad $$- 200$$ rad/s $$t + (1.50$$ rad/s$$^2) t^2$. What is the angular velocity of the motor shaft after 5.0$ s?

Accepted Answer

$$-118$$ rad/s

Question 20

A part of a mechanical linkage has a mass of $$1.5 kg. $$Its moment of inertia $$I$$ about an axis $$0.15 m $$from its center of mass is $$0.132 kg$$\cdot m$$^2. $$What is the moment of inertia $$I_{	ext{total}}$$ about a parallel axis through the center of mass?

Accepted Answer

$$0.085 kg$$\cdot $$m^2$

Physics 111 Exam 3 Practice Problems: Rotation, Dynamics, and Gravitation

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