Question 1

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end.In this collision

Accepted Answer

A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved. 
A) momentum is conserved. 
B) angular momentum is conserved. 
C) energy is conserved. 
D) all of the above are conserved. 
E) only momentum and angular momentum are conserved.

Question 2

A uniform rod (length = 2.0 m)is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod.If the rod is released from rest in a horizontal position,what is the angular speed of the rod as it rotates through its lowest position?

Accepted Answer

A) 3.5 rad/s 
B) 3.8 rad/s 
C) 4.1 rad/s 
D) 2.0 rad/s 
E) 5.6 rad/s 
A) 3.5 rad/s 
B) 3.8 rad/s 
C) 4.1 rad/s 
D) 2.0 rad/s 
E) 5.6 rad/s

Question 3

Particles (mass of each = 0.20 kg)are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the initial angular acceleration of the body?

Accepted Answer

A) 12 rad/s2 
B) 5.9 rad/s2 
C) 8.4 rad/s2 
D) 5.4 rad/s2 
E) 17 rad/s2 
A) 12 rad/s2 
B) 5.9 rad/s2 
C) 8.4 rad/s2 
D) 5.4 rad/s2 
E) 17 rad/s2

Question 4

A wheel (radius = 0.20 m)starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2.At the instant when the angular velocity is equal to 1.2 rad/s,what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

Accepted Answer

A) 0.40 m/s2 
B) 0.29 m/s2 
C) 0.69 m/s2 
D) 0.49 m/s2 
E) 0.35 m/s2 
A) 0.40 m/s2 
B) 0.29 m/s2 
C) 0.69 m/s2 
D) 0.49 m/s2 
E) 0.35 m/s2

Question 5

A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick.The stick is released from rest in a horizontal position.The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML2.Determine the magnitude of the initial angular acceleration of the stick.

Accepted Answer

A) 17 rad/s2 
B) 13 rad/s2 
C) 15 rad/s2 
D) 19 rad/s2 
E) 23 rad/s2 
A) 17 rad/s2 
B) 13 rad/s2 
C) 15 rad/s2 
D) 19 rad/s2 
E) 23 rad/s2

Question 6

A skater extends her arms horizontally,holding a 5-kg mass in each hand.She is rotating about a vertical axis with an angular velocity of one revolution per second.If she drops her hands to her sides,what will the final angular velocity (in rev/s)be if her moment of inertia remains approximately constant at 5 kg.m2,and the distance of the masses from the axis changes from 1 m to 0.1 m?

Accepted Answer

A) 6 
B) 3 
C) 9 
D) 4 
E) 7 
A) 6 
B) 3 
C) 9 
D) 4 
E) 7

Question 7

A cylindrical shell rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

Accepted Answer

A) (5/7)g sin$\theta$ 
B) (1/2)g sin $\theta$ 
C) (3/5)g sin $\theta$ 
D) (2/3)g sin $\theta$ 
E) (4/5)g sin $\theta$ 
A) (5/7)g sin$\theta$ 
B) (1/2)g sin $\theta$ 
C) (3/5)g sin $\theta$ 
D) (2/3)g sin $\theta$ 
E) (4/5)g sin $\theta$

Question 8

A coin with a diameter 3.00 cm rolls up a 30.0$\degree$inclined plane.The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping.If the moment of inertia of the coin is $\frac { 1 } { 2 }$ MR2,how far will the coin roll up the inclined plane?

Accepted Answer

The answer of A coin with a diameter 3.00 cm...

Question 9

A wheel (radius = 0.20 m)is mounted on a frictionless,horizontal axis.A light cord wrapped around the wheel supports a 0.50-kg object,as shown in the figure.When released from rest the object falls with a downward acceleration of 5.0 m/s2.What is the moment of inertia of the wheel?

Accepted Answer

A) 0.023 kg.m2 
B) 0.027 kg.m2 
C) 0.016 kg.m2 
D) 0.019 kgF.m2 
E) 0.032 kg.m2 
A) 0.023 kg.m2 
B) 0.027 kg.m2 
C) 0.016 kg.m2 
D) 0.019 kgF.m2 
E) 0.032 kg.m2

Question 10

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2.In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

Accepted Answer

A) 2.5 s 
B) 4.0 s 
C) 3.5 s 
D) 3.0 s 
E) 4.5 s 
A) 2.5 s 
B) 4.0 s 
C) 3.5 s 
D) 3.0 s 
E) 4.5 s

Question 11

A space station out beyond the solar system is rotating with constant angular velocity.A spaceship heading into the station along a diameter of the station,uses its rockets to brake,and then docks inside the station at its center.When the spaceship docks,the angular momentum of the system consisting of the station and ship

Accepted Answer

A) is less than the original angular momentum of the station. 
B) is the same as the original angular momentum of the station. 
C) is greater than the original angular momentum of the station. 
D) is less than the original angular momentum of the station,but the angular velocity increases. 
E) is greater than the original angular momentum of the station,but the angular velocity decreases. 
A) is less than the original angular momentum of the station. 
B) is the same as the original angular momentum of the station. 
C) is greater than the original angular momentum of the station. 
D) is less than the original angular momentum of the station,but the angular velocity increases. 
E) is greater than the original angular momentum of the station,but the angular velocity decreases.

Question 12

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The change in angular velocity,$\Delta$$ \omega $,during this 8-second period is

Accepted Answer

A)  $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW. 
B)  $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW. 
C)  $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW. 
D)  $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW. 
E)  $31 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW. 
A)  $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW. 
B)  $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW. 
C)  $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW. 
D)  $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW. 
E)  $31 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.

Question 13

A uniform rod (mass = 1.5 kg)is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest in a horizontal position.What is the angular speed of the rod when the rod makes an angle of 30 $\degree$ with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg.m2).

Accepted Answer

A) 2.2 rad/s 
B) 3.6 rad/s 
C) 2.7 rad/s 
D) 3.1 rad/s 
E) 1.8 rad/s 
A) 2.2 rad/s 
B) 3.6 rad/s 
C) 2.7 rad/s 
D) 3.1 rad/s 
E) 1.8 rad/s

Question 14

Two particles (m1 = 0.20 kg,m2 = 0.30 kg)are positioned at the ends of a 2.0-m long rod of negligible mass.What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?

Accepted Answer

A) 0.48 kg.m2 
B) 0.50 kg.m2 
C) 1.2 kg.m2 
D) 0.80 kg.m2 
E) 0.70 kg.m2 
A) 0.48 kg.m2 
B) 0.50 kg.m2 
C) 1.2 kg.m2 
D) 0.80 kg.m2 
E) 0.70 kg.m2

Question 15

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg.m2/s)relative to the origin?

Accepted Answer

A) -30 $$\hat { k }$$ 
B) 30 $\hat { k }$ 
C) -15 $\hat { k }$ 
D) 15 $\hat { k }$ 
E) 45 $\hat { k }$ 
A) -30 $$\hat { k }$$ 
B) 30 $\hat { k }$ 
C) -15 $\hat { k }$ 
D) 15 $\hat { k }$ 
E) 45 $\hat { k }$

Question 16

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t3,where $\theta$ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Accepted Answer

A) -1.0 rad/s2 
B) -24 rad/s2 
C) -2.0 rad/s2 
D) -4.0 rad/s2 
E) -3.5 rad/s2 
A) -1.0 rad/s2 
B) -24 rad/s2 
C) -2.0 rad/s2 
D) -4.0 rad/s2 
E) -3.5 rad/s2

Question 17

The object shown below has mass m and velocity $\overrightarrow { \mathbf { v } }$ .The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is

Accepted Answer

A) downwards. 
B) to the right. 
C) into the page. 
D) up out of the page. 
E) counterclockwise. 
A) downwards. 
B) to the right. 
C) into the page. 
D) up out of the page. 
E) counterclockwise.

Question 18

A uniform rod of length (L = 2.0 m)and mass (M = 1.5 kg)is pivoted about a horizontal frictionless pin through one end.The rod is released from rest at an angle of 30 $\degree$below the horizontal.What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg.m2. )

Accepted Answer

A) 3.5 rad/s 
B) 2.7 rad/s 
C) 3.1 rad/s 
D) 2.3 rad/s 
E) 1.6 rad/s 
A) 3.5 rad/s 
B) 2.7 rad/s 
C) 3.1 rad/s 
D) 2.3 rad/s 
E) 1.6 rad/s

Question 19

A massless rope is wrapped around a uniform cylinder that has radius R and mass M,as shown in the figure.Initially,the unwrapped portion of the rope is vertical and the cylinder is horizontal.The linear acceleration of the cylinder is

Accepted Answer

A) (2/3)g 
B) (1/2)g 
C) (1/3)g 
D) (1/6)g 
E) (5/6)g 
A) (2/3)g 
B) (1/2)g 
C) (1/3)g 
D) (1/6)g 
E) (5/6)g

Question 20

When the sum of the external forces and the sum of the external torques on a body are both zero,we can conclude that

Accepted Answer

A) the body is moving at constant velocity but is not rotating. 
B) the body is rotating at constant angular velocity but has no linear velocity. 
C) the body has neither linear nor angular velocity. 
D) the body may have constant linear or angular velocity,but not both simultaneously. 
E) the body may have constant linear or constant angular velocity,or both simultaneously. 
A) the body is moving at constant velocity but is not rotating. 
B) the body is rotating at constant angular velocity but has no linear velocity. 
C) the body has neither linear nor angular velocity. 
D) the body may have constant linear or angular velocity,but not both simultaneously. 
E) the body may have constant linear or constant angular velocity,or both simultaneously.

Exam 10: Rotational Motion

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end.In this collision

Particles (mass of each = 0.20 kg)are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the initial angular acceleration of the body?

A wheel (radius = 0.20 m)starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2.At the instant when the angular velocity is equal to 1.2 rad/s,what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

A cylindrical shell rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

A wheel (radius = 0.20 m)is mounted on a frictionless,horizontal axis.A light cord wrapped around the wheel supports a 0.50-kg object,as shown in the figure.When released from rest the object falls with a downward acceleration of 5.0 m/s2.What is the moment of inertia of the wheel?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2.In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The change in angular velocity, Δ\DeltaΔω \omega ω ,during this 8-second period is

Two particles (m1 = 0.20 kg,m2 = 0.30 kg)are positioned at the ends of a 2.0-m long rod of negligible mass.What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg.m2/s)relative to the origin?

A wheel rotating about a fixed axis has an angular position given by θ\thetaθ = 3.0 -2.0t3,where θ\thetaθ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

The object shown below has mass m and velocity v→\overrightarrow { \mathbf { v } }v .The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is

A massless rope is wrapped around a uniform cylinder that has radius R and mass M,as shown in the figure.Initially,the unwrapped portion of the rope is vertical and the cylinder is horizontal.The linear acceleration of the cylinder is

When the sum of the external forces and the sum of the external torques on a body are both zero,we can conclude that

Introduction and Vectors

Motion in One Dimension

Motion in Two Dimensions

The Laws of Motion

More Applications of Newtons Laws

Energy of a System

Conservation of Energy

Momentum and Collisions

Relativity

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Oscillatory Motion

Mechanical Waves

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Fluid Mechanics

Temperature and the Kinetic Theory of Gases

Energy in Thermal Processes: the First Law of Thermodynamics

Heat Engines,entropy,and the Second Law of Thermodynamics

Electric Forces and Electric Fields

Electric Potential and Capacitance

Current and Direct Current Circuits

Magnetic Forces and Magnetic Fields

Faradays Law and Inductance

Electromagnetic Waves

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Filters

A wheel (radius = 0.20 m)starts from rest and rotates with a constant angular acceleration of 2.0 rad/s².At the instant when the angular velocity is equal to 1.2 rad/s,what is the magnitude of the total linear acceleration of a point on the rim of the wheel?

A wheel (radius = 0.20 m)is mounted on a frictionless,horizontal axis.A light cord wrapped around the wheel supports a 0.50-kg object,as shown in the figure.When released from rest the object falls with a downward acceleration of 5.0 m/s².What is the moment of inertia of the wheel?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s².In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

Two particles (m₁ = 0.20 kg,m₂ = 0.30 kg)are positioned at the ends of a 2.0-m long rod of negligible mass.What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5.What is its angular momentum (in kg.m²/s)relative to the origin?

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t³,where $\theta$ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?