Question 1

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 1011 m. What is the diameter of the sun?

Accepted Answer

Question 2

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

Accepted Answer

A)  0.616 rad/s2 
B)  5.45 rad/s2 
C)  111 rad/s2 
D)  22.5 rad/s2 
E)  10.9 rad/s2 
A)  0.616 rad/s2 
B)  5.45 rad/s2 
C)  111 rad/s2 
D)  22.5 rad/s2 
E)  10.9 rad/s2

Question 3

A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board. How far from the man is the center of mass (or center of gravity) of the man-board system?

Accepted Answer

A)  1.25 m 
B)  2.50 m 
C)  5.00 m 
D)  7.50 m 
E)  9.00 m 
A)  1.25 m 
B)  2.50 m 
C)  5.00 m 
D)  7.50 m 
E)  9.00 m

Question 4

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees does the cylinder turn during this time?

Accepted Answer

The answer of A cylinder of radius 8.0 cm rolls...

Question 5

A force of $16.88 \mathrm {~N}$ is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?

Accepted Answer

A)  4.78 kg ? m2 
B)  3.59 kg ? m2 
C)  5.98 kg ? m2 
D)  7.17 kg ? m2 
A)  4.78 kg ? m2 
B)  3.59 kg ? m2 
C)  5.98 kg ? m2 
D)  7.17 kg ? m2

Question 6

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 $\mathrm { kg } \cdot \mathrm { m } ^ { 2 }$ about an axis perpendicular to it through its center. The frictional torque at the drum axle is 3.0 N ? m. A 14-m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum is $23 \mathrm { rad } / \mathrm { s }$ The drum then slows down at a constant rate and comes to a halt. In this situation, what was the magnitude of the constant force applied to the rope?

Accepted Answer

A)  51 N 
B)  40 N 
C)  29 N 
D)  18 N 
E)  7.5 N 
A)  51 N 
B)  40 N 
C)  29 N 
D)  18 N 
E)  7.5 N

Question 7

In the figure, four point masses are placed as shown. Assume that all the numbers in the figure are accurate to two significant figures. What are the x and y coordinates of the center of mass (or center of gravity) of this arrangement?

Accepted Answer

A)  (2.2 m, 2.6 m) 
B)  (2.2 m, 2.7 m) 
C)  (2.3 m, 2.6 m) 
D)  (2.3 m, 2.7 m) 
E)  (2.3 m, 2.8 m) 
A)  (2.2 m, 2.6 m) 
B)  (2.2 m, 2.7 m) 
C)  (2.3 m, 2.6 m) 
D)  (2.3 m, 2.7 m) 
E)  (2.3 m, 2.8 m)

Question 8

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest.
(a) What was the magnitude of the angular acceleration of the centrifuge as it slowed down?
(d) How long did it take for the centrifuge to come to rest after being turned off?

Accepted Answer

(a) 230 ra

Question 9

Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity) of the system?

Accepted Answer

A)  (1 m, 2 m) 
B)  (2 m, 1 m) 
C)  (1 m, 1 m) 
D)  (1 m, 0.5 m) 
E)  (0.5 m, 1 m) 
A)  (1 m, 2 m) 
B)  (2 m, 1 m) 
C)  (1 m, 1 m) 
D)  (1 m, 0.5 m) 
E)  (0.5 m, 1 m)

Question 10

The diameter of the Moon is 3.47 × 106 m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?

Accepted Answer

Question 11

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

Accepted Answer

A)  10.4 rad/s2 
B)  20.8 rad/s2 
C)  5.20 rad/s2 
D)  3.43 rad/s2 
E)  1.06 rad/s2 
A)  10.4 rad/s2 
B)  20.8 rad/s2 
C)  5.20 rad/s2 
D)  3.43 rad/s2 
E)  1.06 rad/s2

Question 12

Three balls are moving along a straight line having the instantaneous positions shown in the figure. At that instant, find the location and velocity of the center of mass (or center of gravity) of this system.

Accepted Answer

7.00 m to the right

Question 13

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s2 when it is released, what is the mass M of the pulley?

Accepted Answer

A)  2.0 kg 
B)  4.0 kg 
C)  6.0 kg 
D)  8.0 kg 
E)  10 kg 
A)  2.0 kg 
B)  4.0 kg 
C)  6.0 kg 
D)  8.0 kg 
E)  10 kg

Question 14

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of mass (or center of gravity) of this system.

Accepted Answer

A)  (0.50 m, 1.5 m) 
B)  (1.5 m, 0.50 m) 
C)  (2.5 m, 1.5 m) 
D)  (2.5 m, 0.50 m) 
A)  (0.50 m, 1.5 m) 
B)  (1.5 m, 0.50 m) 
C)  (2.5 m, 1.5 m) 
D)  (2.5 m, 0.50 m)

Question 15

A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?

Accepted Answer

A)  5.64 m/s 
B)  3.50 m/s 
C)  0.556 m/s 
D)  1.75 m/s 
E)  1.80 m/s 
A)  5.64 m/s 
B)  3.50 m/s 
C)  0.556 m/s 
D)  1.75 m/s 
E)  1.80 m/s

Question 16

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° 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

A)  7.6 N ∙ m 
B)  10.7 N ∙ m 
C)  12.0 N ∙ m 
D)  9.7 N ∙ m 
A)  7.6 N ∙ m 
B)  10.7 N ∙ m 
C)  12.0 N ∙ m 
D)  9.7 N ∙ m

Question 17

As shown in the figure, a 60-cm length of uniform wire, of mass 60 g, is bent into a right triangle. What are the x and y coordinates of the center of mass (or center of gravity) of this triangle?

Accepted Answer

A)  (8.0 cm, 3.0 cm) 
B)  (8.0 cm, 5.0 cm) 
C)  (9.0 cm, 4.0 cm) 
D)  (10 cm, 3.0 cm) 
E)  (10 cm, 5.0 cm) 
A)  (8.0 cm, 3.0 cm) 
B)  (8.0 cm, 5.0 cm) 
C)  (9.0 cm, 4.0 cm) 
D)  (10 cm, 3.0 cm) 
E)  (10 cm, 5.0 cm)

Question 18

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s.
(a) Through what angle does the bowling ball turn as it travels the length of the lane?
(b) What is the angular speed of the bowling ball?
(c) Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have.
(d) Calculate the tangential acceleration of a point on the surface of the bowling ball.

Accepted Answer

(a) 110 ra

Question 19

In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses.

Accepted Answer

The answer of In the figure, a weightlifter's barbell consists...

Question 20

As shown in the figure, a 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m2. 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

A)  2.97 s 
B)  2.85 s 
C)  0.892 s 
D)  4.18 s 
E)  5.89 s 
A)  2.97 s 
B)  2.85 s 
C)  0.892 s 
D)  4.18 s 
E)  5.89 s

Exam 7: Rotational Motion

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 1011 m. What is the diameter of the sun?

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board. How far from the man is the center of mass (or center of gravity) of the man-board system?

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees does the cylinder turn during this time?

A force of 16.88 N16.88 \mathrm {~N}16.88 N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?

In the figure, four point masses are placed as shown. Assume that all the numbers in the figure are accurate to two significant figures. What are the x and y coordinates of the center of mass (or center of gravity) of this arrangement?

Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity) of the system?

The diameter of the Moon is 3.47 × 106 m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

Three balls are moving along a straight line having the instantaneous positions shown in the figure. At that instant, find the location and velocity of the center of mass (or center of gravity) of this system.

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s2 when it is released, what is the mass M of the pulley?

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of mass (or center of gravity) of this system.

A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° 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?

As shown in the figure, a 60-cm length of uniform wire, of mass 60 g, is bent into a right triangle. What are the x and y coordinates of the center of mass (or center of gravity) of this triangle?

Representing Motion

Motion in One Dimension

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Forces and Newtons Laws of Motion

Applying Newtons Laws

Gravity

Equilibrium Ad Elasticity

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Energy and Work

Using Energy

Thermal Properties of Matter

Fluids

Oscillations

Traveling Waves and Sound

Superposition and Standing Waves

Wave Optics

Ray Optics

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EM Induction and Em Waves

AC Electricity

Relativity

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Filters

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 10¹¹m. What is the diameter of the sun?

A force of $16.88 \mathrm {~N}$ is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s². What is the moment of inertia of the wheel?

The diameter of the Moon is 3.47 × 10⁶ m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s² when it is released, what is the mass M of the pulley?