Q: A force $$\vec{F} = (-5.00\hat{i} + 4.00\hat{j}) N $$acts at position $$\vec{r} = (-0.450\hat{i} + 0.150\hat{j}) m. $$What is the torque vector about the origin?

$$\vec{\tau} = -1.05\hat{k} N$$·m

Question 1

A 3.0-kg ball with an initial velocity of $$\vec{v}_i = (4\hat{i} + 3\hat{j}) m/s $$collides with a wall and rebounds with a velocity of $$\vec{v}_f = (-4\hat{i} + 3\hat{j}) m/s. $$What is the impulse exerted on the ball by the wall?

Accepted Answer

$$-24\hat{i} N$$·s

Question 2

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

Accepted Answer

$$36 m/s$$

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 $$2$$ revolutions?

Accepted Answer

$$4 s$$

Question 4

A wheel with radius $$R = 0.5 m$$, initially spinning at $$2.5$$ rev/s, slows down at $$2$$ rad/s$$^2. By $$the time it stops, what distance will a point on the outer rim have traveled?

Accepted Answer

$$31 m$$

Question 5

A solid ball of mass $$0.25 kg $$rolls without slipping $$4 m $$down an incline at $$25^\circ$$ with the horizontal, starting from rest. What is its kinetic energy at the bottom of the incline?

Accepted Answer

$$4 J$$

Question 6

A basketball (hollow shell, $$I = \frac{2}{3}mr^2$) is rolling without slipping with total kinetic energy 20$ J. How much energy is due to rotational kinetic energy?

Accepted Answer

$$8 J$$

Question 7

A hollow spherical shell of mass $$2.00 kg $$rolls without slipping down a $$38.0^\circ$$ slope. What is the minimum coefficient of static friction needed to prevent slipping?

Accepted Answer

$$0.313$$

Question 8

A $$10-kg $$bicycle wheel (thin hoop, $$I = mr^2$, r = 0.5$ m) is rotating at 60$ rev/min. How much work must be done to bring it to a stop?

Accepted Answer

$$49.35 J$$

Question 9

You throw a $$0.40 kg $$ball horizontally to the left at $$30 m/s $$against a wall. It rebounds to the right at $$20 m/s. $$What is the impulse of the net external force on the ball during the collision?

Accepted Answer

$$20 N$$\cdot s$

Question 10

If the ball in the previous problem is in contact with the wall for $$0.010 s$$, what is the average horizontal force that the wall exerts on the ball during the impact?

Accepted Answer

$$2000 N$$

Question 11

Two small spheres, each of mass $$0.0200 kg$$, are connected by a $$1.60 m $$rod and rotate about an axis at the center. If the total kinetic energy is $$1.28 J$$, what is the angular speed in rad/s?

Accepted Answer

$$10$$

Question 12

The mass of the Sun is $$2.0 	imes 10$$^{30}$$ kg and the mass of the Earth is 6.0$$ 	imes $$10^{24} kg. If $$the distance between them is $$1.50 	imes 10^8$ km, how far from the center of the Sun is the center of mass of the Sun-Earth system?

Accepted Answer

$$450 km$$

Question 13

A playground merry-go-round has a radius of $$3.0 m $$and a rotational inertia of $$600 kg$$·m$$^2. It is $$spinning at $$0.80$$ rad/s when a $$20-kg $$child crawls from the center to the rim. What is the new angular velocity when the child reaches the rim?

Accepted Answer

$$0.61$$ rad/s

Question 14

A system consists of three particles with masses $$m_1$$ = $$m_2 = 1.0$ kg and m_3$ = 2.0 kg $$located as shown in the figure. What are the coordinates of the center of mass?

Accepted Answer

$$x_{cm} = 0.75 m$$, $$y_{cm} = 1.0 m$$

Question 15

A force $$\vec{F} = (-5.00\hat{i} + 4.00\hat{j}) N $$acts at position $$\vec{r} = (-0.450\hat{i} + 0.150\hat{j}) m. $$What is the torque vector about the origin?

Accepted Answer

$$\vec{	au} = -1.05\hat{k} N$$·m

Question 16

A bullet of mass $$7.54 g is $$fired into a $$4.0 kg $$wooden block on a horizontal surface. The bullet gets stuck and the block moves at $$2.5 m/s. $$What was the original speed of the bullet?

Accepted Answer

$$1330 m/s$$

Question 17

A $$6 kg $$particle with velocity $$\vec{v} = -2\hat{i} + 5\hat{j} is at$$ $$x = 30 m$$, $$y = 45 m. $$What is the angular momentum of the particle about the origin?

Accepted Answer

$$1440\hat{k} kg$$·m$$^2/s$$

Question 18

A wheel is rotating freely at $$900$$ rev/min on a shaft with negligible inertia. A second wheel, initially at rest and with three times the rotational inertia, is suddenly coupled to the shaft. What is the angular speed of the combination?

Accepted Answer

$$225$$ rev/min

Question 19

A part of a mechanical linkage has mass $$3.6 kg. $$Its moment of inertia about an axis $$0.15 m $$from its center of mass is $$I_P = 0.132 kg$$·m$$^2. $$What is the moment of inertia about a parallel axis through the center of mass?

Accepted Answer

$$0.051 kg$$·m$$^2$$

Physics 111 Exam 3 Study Guidance: Impulse, Collisions, Rotational Motion, Center of Mass, and Moment of Inertia

Study Guide - Practice Questions

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