Question 1

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

A celestial object called a pulsar emits its light in short bursts that are synchronised with its rotation. A pulsar in the Crab Nebula is rotating at a rate of 30 revolutions/second. What is the maximum radius of the pulsar, if no part of its surface can move faster than the speed of light (3 *108 m/s)?

Accepted Answer

The answer of A celestial object called a pulsar emits...

Question 3

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The angular velocity at t = 0 s is $\omega_{0}=5 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CCW. The angular velocity, $ \omega $, at t = 8 s 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)  $43 \frac{\mathrm{rad}}{\mathrm{~s}}$ , 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)  $43 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW.

Question 4

Imagine that you are at Luna Park having a ride on a carousel. As you go round and round, you look up and see that a seagull is flying in a circle directly over your head. As you go around in a circle, so does the seagull, so that it remains directly over you. Naturally you are a bit freaked out by this, and you start to wonder if the seagull has taken a dislike to you, and plans to do a dropping on your head. Will a dropping the bird releases while flying directly above your head hit you?

Accepted Answer

A) Yes, because it falls straight down. 
B) Yes, because it maintains the acceleration of the bird as it falls. 
C) No, because it falls straight down and will land behind the person. 
D) Yes, because it maintains the angular velocity of the bird as it falls. 
E) No, because it maintains the tangential velocity the bird had at the instant it started falling. 
A) Yes, because it falls straight down. 
B) Yes, because it maintains the acceleration of the bird as it falls. 
C) No, because it falls straight down and will land behind the person. 
D) Yes, because it maintains the angular velocity of the bird as it falls. 
E) No, because it maintains the tangential velocity the bird had at the instant it started falling.

Question 5

A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the centre of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s2. What is the moment of inertia (of the wheel) about the given axle?

Accepted Answer

A) 0.023 kg.m2 
B) 0.013 kg.m2 
C) 0.020 kg.m2 
D) 0.016 kg.m2 
E) 0.035 kg.m2 
A) 0.023 kg.m2 
B) 0.013 kg.m2 
C) 0.020 kg.m2 
D) 0.016 kg.m2 
E) 0.035 kg.m2

Question 6

A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg.m2. The cord does not slip on the pulley. What is the magnitude of the acceleration of m?

Accepted Answer

A) 2.4 m/s2 
B) 2.8 m/s2 
C) 3.2 m/s2 
D) 4.2 m/s2 
E) 1.7 m/s2 
A) 2.4 m/s2 
B) 2.8 m/s2 
C) 3.2 m/s2 
D) 4.2 m/s2 
E) 1.7 m/s2

Question 7

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track.   What is his average angular acceleration, in rad/s2, in the first 10 minutes?

Accepted Answer

A) 0 
B)  $-\frac{\pi}{150}$ 
C)  $-\frac{\pi}{75}$ 
D)  $+\frac{\pi}{75}$ 
E)  $+\frac{\pi}{150}$ 
A) 0 
B)  $-\frac{\pi}{150}$ 
C)  $-\frac{\pi}{75}$ 
D)  $+\frac{\pi}{75}$ 
E)  $+\frac{\pi}{150}$

Question 8

Particles (mass of each = 0.20 kg) are placed at the 40-cm and 100-cm marks of a metre 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 9

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Accepted Answer

A) 30 
B) 50 
C) 70 
D) 90 
E) 100 
A) 30 
B) 50 
C) 70 
D) 90 
E) 100

Question 10

Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track.   What is her angular displacement (in rad) in the first 8 minutes?

Accepted Answer

A) 0 
B) ( $\pi$) 
C) 4 $\pi$ 
D) 8 $\pi$ 
E) 16 $\pi$ 
A) 0 
B) ( $\pi$) 
C) 4 $\pi$ 
D) 8 $\pi$ 
E) 16 $\pi$

Question 11

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track.   What is his average angular acceleration, in rad/s2, in the period from t = 6 min to t = 8 min?

Accepted Answer

A) 0 
B)  $-\frac{\pi}{90}$ 
C)  $-\frac{\pi}{30}$ 
D)  $+\frac{\pi}{30}$ 
E)  $+\frac{\pi}{90}$ 
A) 0 
B)  $-\frac{\pi}{90}$ 
C)  $-\frac{\pi}{30}$ 
D)  $+\frac{\pi}{30}$ 
E)  $+\frac{\pi}{90}$

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

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track.   How many revolutions does she complete in the 16-minute period?

Accepted Answer

A) 8 
B) 12 
C) 16 
D) 20 
E) 40 
A) 8 
B) 12 
C) 16 
D) 20 
E) 40

Question 14

A uniform metre 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 centre 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 15

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 centre 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 16

A rod of length 1.00 m has a mass per unit length given by $\lambda=2.00+1.00 x^{2}$ , where $\lambda$ is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg $\cdot$ m2 about the y axis?

Accepted Answer

The answer of A rod of length 1.00 m has...

Question 17

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track.   What is her angular displacement (in rad) in the first 12 minutes?

Accepted Answer

A) 0 
B) 2 $\pi$ 
C) 4 $\pi$ 
D) 16 $\pi$ 
E) 32 $\pi$ 
A) 0 
B) 2 $\pi$ 
C) 4 $\pi$ 
D) 16 $\pi$ 
E) 32 $\pi$

Question 18

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

Question 19

The angular speed of the hour hand of a clock, in rad/s, is:

Accepted Answer

A)  $\frac{1}{7200} \pi$ . 
B)  $\frac{1}{1800} \pi$ . 
C)  $\frac{1}{30} \pi$ . 
D) 1 800 $\pi$. 
E) 7 200 $\pi$. 
A)  $\frac{1}{7200} \pi$ . 
B)  $\frac{1}{1800} \pi$ . 
C)  $\frac{1}{30} \pi$ . 
D) 1 800 $\pi$. 
E) 7 200 $\pi$.

Question 20

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval?

Accepted Answer

A) 9.5 rad/s 
B) 9.7 rad/s 
C) 9.3 rad/s 
D) 9.1 rad/s 
E) 8.8 rad/s 
A) 9.5 rad/s 
B) 9.7 rad/s 
C) 9.3 rad/s 
D) 9.1 rad/s 
E) 8.8 rad/s

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track. What is his average angular acceleration, in rad/s2, in the first 10 minutes?

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. What is her angular displacement (in rad) in the first 8 minutes?

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track. What is his average angular acceleration, in rad/s2, in the period from t = 6 min to t = 8 min?

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. How many revolutions does she complete in the 16-minute period?

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 centre of mass?

A rod of length 1.00 m has a mass per unit length given by $\lambda=2.00+1.00 x^{2}$ , where $\lambda$ is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg $\cdot$ m² about the y axis?

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. What is her angular displacement (in rad) in the first 12 minutes?

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?

The angular speed of the hour hand of a clock, in rad/s, is:

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval?

Physics and Measurement

Motion in One Dimension

Motion in Two Dimensions

Forces and Newtons Laws

Further Applications of Newtons Laws

Work, Force and Energy

Conservation of Energy

Linear Momentum and Collisions

Energy and Momentum in Rotating Systems

Gravity

Special Relativity

Fluid Statics

Fluid Dynamics

Solids

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Exam 9: Rotational Motion

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The angular velocity at t = 0 s is ω0=5rad s\omega_{0}=5 \frac{\mathrm{rad}}{\mathrm{~s}}ω0​=5 srad​ , CCW. The angular velocity, ω \omega ω , at t = 8 s is:

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track. What is his average angular acceleration, in rad/s2, in the first 10 minutes?

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. What is her angular displacement (in rad) in the first 8 minutes?

Refer to Exhibit 9-2 below.Exhibit 9-2 The figure below shows a graph of angular velocity versus time for a man cycling around a circular track. What is his average angular acceleration, in rad/s2, in the period from t = 6 min to t = 8 min?

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:

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. How many revolutions does she complete in the 16-minute period?

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 centre of mass?

A rod of length 1.00 m has a mass per unit length given by λ=2.00+1.00x2\lambda=2.00+1.00 x^{2}λ=2.00+1.00x2 , where λ\lambdaλ is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg ⋅\cdot⋅ m2 about the y axis?

Refer to Exhibit 9-1 below.Exhibit 9-1 The figure below shows a graph of angular velocity versus time for a woman cycling around a circular track. What is her angular displacement (in rad) in the first 12 minutes?

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?

The angular speed of the hour hand of a clock, in rad/s, is:

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval?

Physics and Measurement

Motion in One Dimension

Motion in Two Dimensions

Forces and Newtons Laws

Further Applications of Newtons Laws

Work, Force and Energy

Conservation of Energy

Linear Momentum and Collisions

Energy and Momentum in Rotating Systems

Gravity

Special Relativity

Fluid Statics

Fluid Dynamics

Solids

Oscillatory Motion

Wave Motion

Superposition and Interference

Heat and Temperature

Energy Transfer Processes and Thermodynamics

The Kinetic Theory of Gases

The Second Law of Thermodynamics, Heat Engines and Entropy

Filters

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 centre of mass?

A rod of length 1.00 m has a mass per unit length given by $\lambda=2.00+1.00 x^{2}$ , where $\lambda$ is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg $\cdot$ m² about the y axis?