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 × 10¹¹m.What is the diameter of the sun?

Accepted Answer

The answer of The sun subtends an angle of 0.00928...

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

Question 3

The figure shows two blocks connected by a light cord over a pulley.This apparatus is known as an Atwood's machine.There is no slipping between the cord and the surface of the pulley.The pulley itself has negligible friction and it has a radius of 0.12 m and a mass of 10.3 kg.We can model this pulley as a solid uniform disk.At the instant that the heavier block has descended 1.5 m starting from rest,what is the speed of the lighter block?

Accepted Answer

The answer of The figure shows two blocks connected by...

Question 4

A wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s.(a)Through what angle does the wheel turn in the first 2.0 s,and (b)what is its angular speed at that time?

Accepted Answer

The answer of A wheel accelerates with a constant angular...

Question 5

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

Accepted Answer

A) 100 rad/s 
B) 50 rad/s 
C) 25 rad/s 
D) 20 rad/s 
E) 10 rad/s

Question 6

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

Accepted Answer

A) higher than when it was released. 
B) lower than when it was released. 
C) at the same height from which it was released. 
D) It is impossible to tell without knowing the mass of the ball. 
E) It is impossible to tell without knowing the radius of the ball.

Question 7

A ballerina spins initially at 1.5 rev/s when her arms are extended.She then draws in her arms to her body and her moment of inertia becomes 0.88 kg ∙ m²,and her angular speed increases to 4.0 rev/s.What was her initial moment of inertia?

Accepted Answer

The answer of A ballerina spins initially at 1.5 rev/s...

Question 8

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere.

Question 9

In a certain cyclotron,a proton of mass 1.67 × 10-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 106 rad/s.What is the angular momentum of the proton?

Accepted Answer

A) 1.3 × 10-21 kg ∙ m2/s 
B) 1.8 × 10-21 kg ∙ m2/s 
C) 2.1 × 10-21 kg ∙ m2/s 
D) 3.2 × 10-21 kg ∙ m2/s

Question 10

Consider a uniform hoop of radius R and mass M rolling without slipping.Which is larger,its translational kinetic energy or its rotational kinetic energy?

Accepted Answer

A) Translational kinetic energy is larger. 
B) Rotational kinetic energy is larger. 
C) Both are equal. 
D) You need to know the speed of the hoop to tell.

Question 11

A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm.This pulley is frictionless in its axle,and has the shape of a solid uniform disk.After the bucket has been released,(a)what is the angular acceleration of the pulley,and (b)what is the acceleration of the bucket?

Accepted Answer

The answer of A 1.53-kg bucket hangs on a rope...

Question 12

In the figure,point P is on the rim of a wheel of radius 2.0 m.At time t = 0,the wheel is at rest,and P is on the x-axis.The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s² about the center O. (a)At time t = 0,what is the tangential acceleration of P? (b)What is the linear speed of P when it reaches the y-axis? (c)What is the magnitude of the net linear acceleration of P when it reaches the y-axis? (d)How long after starting does it take for P to return to its original position on the x-axis?

Accepted Answer

The answer of In the figure,point P is on the...

Question 13

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?

Accepted Answer

A) The hoop 
B) The disk 
C) Both reach the bottom at the same time.

Question 14

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Accepted Answer

The answer of Express the angular speed of an old...

Question 15

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2.If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m2,what will be his new angular speed?

Accepted Answer

A) 2.25 rad/s 
B) 4.60 rad/s 
C) 6.25 rad/s 
D) 0.81 rad/s

Question 16

A machinist turns on the power on to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $96 \mathrm { rad } / \mathrm { s } .$ The wheel is run at that angular velocity for 40 s and then power is shut off.The wheel slows down uniformly at $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops.For how long a time after the power is shut off does it take the wheel to stop?

Accepted Answer

A) 64 s 
B) 62 s 
C) 66 s 
D) 68 s 
E) 70 s

Question 17

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

Accepted Answer

A) 47.7 rpm 
B) 955 rpm 
C) 72.0 rpm 
D) 50.0 rpm 
E) 100 rpm

Question 18

A small 355-g box hangs from one end of a thin light string that goes over a frictionless pulley having a moment of inertia of 0.0125 kg ∙ m² and a radius of 15 cm.A second small package,this one of mass 680 g,hangs from the other end of the string.When the packages are released,the larger one accelerates downward,the lighter one accelerates upward,and the pulley turns without the string slipping. (a)What is the force that the string on the side of the 355-g package exerts on that package? (b)At what rate do the packages change their speeds?

Accepted Answer

The answer of A small 355-g box hangs from one...

Question 19

When is the angular momentum of a system constant?

Accepted Answer

A) Only when its total kinetic energy is constant. 
B) Only when the linear momentum and the energy are constant. 
C) Only when no net external torque is exerted on the system. 
D) Only when the moment of inertia is constant.

Question 20

In the figure,a weightlifter's barbell consists of two identical small but dense spherical objects,each of mass 50 kg.These objects 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 objects are small enough to be treated as point like objects.

Accepted Answer

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

Exam 9: 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 × 10¹¹m.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 wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s.(a)Through what angle does the wheel turn in the first 2.0 s,and (b)what is its angular speed at that time?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

A ballerina spins initially at 1.5 rev/s when her arms are extended.She then draws in her arms to her body and her moment of inertia becomes 0.88 kg ∙ m²,and her angular speed increases to 4.0 rev/s.What was her initial moment of inertia?

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

In a certain cyclotron,a proton of mass 1.67 × 10^-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 10⁶ rad/s.What is the angular momentum of the proton?

Consider a uniform hoop of radius R and mass M rolling without slipping.Which is larger,its translational kinetic energy or its rotational kinetic energy?

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m².If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m²,what will be his new angular speed?

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

When is the angular momentum of a system constant?

Exam 9: 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 wheel accelerates with a constant angular acceleration of 4.5 rad/s2 from an initial angular speed of 1.0 rad/s.(a)Through what angle does the wheel turn in the first 2.0 s,and (b)what is its angular speed at that time?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

A ballerina spins initially at 1.5 rev/s when her arms are extended.She then draws in her arms to her body and her moment of inertia becomes 0.88 kg ∙ m2,and her angular speed increases to 4.0 rev/s.What was her initial moment of inertia?

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

In a certain cyclotron,a proton of mass 1.67 × 10-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 106 rad/s.What is the angular momentum of the proton?

Consider a uniform hoop of radius R and mass M rolling without slipping.Which is larger,its translational kinetic energy or its rotational kinetic energy?

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2.If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m2,what will be his new angular speed?

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

When is the angular momentum of a system constant?

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 wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s.(a)Through what angle does the wheel turn in the first 2.0 s,and (b)what is its angular speed at that time?

A ballerina spins initially at 1.5 rev/s when her arms are extended.She then draws in her arms to her body and her moment of inertia becomes 0.88 kg ∙ m²,and her angular speed increases to 4.0 rev/s.What was her initial moment of inertia?

In a certain cyclotron,a proton of mass 1.67 × 10^-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 10⁶ rad/s.What is the angular momentum of the proton?

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m².If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m²,what will be his new angular speed?