Question 1

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?
A)0
B)16 $\pi$
C)32 $\pi$
D)40 $\pi$
E)64 $\pi$

Accepted Answer

D

Question 2

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?
A)20 rev
B)24 rev
C)32 rev
D)28 rev
E)39 rev

Accepted Answer

The total number of revolutions can be found using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $t$ is the time. First, find the angular acceleration $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{40 \text{ rad/s} - 20 \text{ rad/s}}{5.0 \text{ s}} = 4 \text{ rad/s}^2$. Then, calculate the angular displacement in radians: $\theta = 20 \text{ rad/s} \times 5.0 \text{ s} + \frac{1}{2} \times 4 \text{ rad/s}^2 \times (5.0 \text{ s})^2 = 100 + 50 = 150 \text{ rad}$. Convert this to revolutions: $150 \text{ rad} \times \frac{1 \text{ rev}}{2\pi \text{ rad}} \approx 24 \text{ rev}$.

Question 3

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel? A)17 rad/s² B)14 rad/s² C)20 rad/s² D)23 rad/s² E)13 rad/s²

Accepted Answer

B

Question 4

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?
A)8
B)12
C)16
D)20
E)40

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 5

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?
A)4
B)8
C)12
D)16
E)32

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 6

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?
A)95 rad
B)85 rad
C)65 rad
D)75 rad
E)125 rad

Accepted Answer

The wheel turns through 75 radians. This can be calculated using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $t$ is the time, and $\alpha$ is the angular acceleration. First, find the angular acceleration using $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{10 \, \text{rad/s} - 20 \, \text{rad/s}}{5.0 \, \text{s}} = -2 \, \text{rad/s}^2$. Then, calculate the angular displacement: $\theta = 20 \, \text{rad/s} \times 5.0 \, \text{s} + \frac{1}{2} \times (-2 \, \text{rad/s}^2) \times (5.0 \, \text{s})^2 = 100 \, \text{rad} - 25 \, \text{rad} = 75 \, \text{rad}$.

Question 7

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? 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

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Question 8

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?
A)0
B) $\pi$
C)4 $\pi$
D)8 $\pi$
E)16 $\pi$

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 9

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

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Question 10

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s? A)4.9 rad B)4.7 rad C)4.5 rad D)4.3 rad E)4.1 rad

Accepted Answer

The answer of At t = 0,a wheel rotating about...

Question 11

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.
A)12 rad
B)8.0 rad
C)10 rad
D)16 rad
E)6.8 rad

Accepted Answer

Using the formula:

$\Delta 	heta = \omega_i t + \frac{1}{2} \alpha t^2$

Where:
$\omega_i = 8.0 	ext{ rad/s}$
$t = 2.5	ext{ s}$
$\alpha = -\frac{\omega_i}{t}$ (since the turntable is slowing down, its acceleration is negative)

We have:

$\Delta 	heta = (8.0	ext{ rad/s})(2.5	ext{ s}) + \frac{1}{2} \left(-\frac{8.0	ext{ rad/s}}{2.5	ext{ s}}ight)(2.5	ext{ s})^2 = 10	ext{ rad}$

Therefore, the answer is (C) 10 rad.

Question 12

The angular speed of the hour hand of a clock,in rad/s,is
A) $\frac { 1 } { 7200 } \pi$ .
B) $\frac { 1 } { 1800 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D)1 800 $\pi$.
E)7 200 $\pi$.

Accepted Answer

The answer of The angular speed of the hour hand...

Question 13

The angular speed of the minute hand of a clock,in rad/s,is
A) $\frac { 1 } { 1800 } \pi$ .
B) $\frac { 1 } { 60 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D) $\pi$.
E)120 $\pi$.

Accepted Answer

The answer of The angular speed of the minute hand...

Question 14

The angular speed of the hour hand of a clock,in rad/min,is
A) $\frac { 1 } { 1800 } \pi$ .
B) $\frac { 1 } { 60 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D) $\pi$.
E)120 $\pi$.

Accepted Answer

The answer of The angular speed of the hour hand...

Question 15

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

Accepted Answer

The answer of The figure below shows a graph of...

Question 16

The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The graphs below show angular velocity as...

Question 17

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s²,in the first 10 minutes? A)0 B) $- \frac { \pi } { 150 }$ C) $- \frac { \pi } { 75 }$ D) $+ \frac { \pi } { 75 }$ E) $+ \frac { \pi } { 150 }$

Accepted Answer

The answer of Exhibit 10-2 The figure below shows a...

Question 18

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?
A)0
B)2 $\pi$
C)4 $\pi$
D)16 $\pi$
E)32 $\pi$

Accepted Answer

The angular displacement is calculated using the formula θ = ωt, where ω is the angular velocity and t is the time. The problem likely provides information that leads to the calculation of 32π radians for the first 12 minutes.

Question 19

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?
A)9.9 s
B)7.8 s
C)8.5 s
D)9.2 s
E)6.4 s

Accepted Answer

Let the angular acceleration be represented by α in rad/s^2 and let the time taken to complete the second revolution be t.

During the first revolution, the angular displacement of the wheel is 2π radians and the time taken is 6 seconds.

Using the formula:
θ = ωi * t + 1/2 * α * t^2
where θ = 2π, ωi = 0 (as the wheel starts from rest), and t = 6 seconds

2π = 0 + 1/2 * α * (6)^2
2π = 18α
α = π/9 rad/s^2

Now, using the same formula for the second revolution, we have:
θ = ωi * t + 1/2 * α * t^2
where θ = 4π (as it completes two revolutions), ωi = 0 (as it starts from rest), and α = π/9 rad/s^2

4π = 0 + 1/2 * (π/9) * t^2
t^2 = 72
t = 8.5 seconds

Therefore, the wheel will complete the second revolution 8.5 seconds after it started. Thus, the best choice is C.

Question 20

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

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Quiz 10: Rotational Motion

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

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?

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?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

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

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

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

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?

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

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

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?

Quiz 10: Rotational Motion

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the 16 minute period shown in the graph?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

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?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the first 8 minutes?

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?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

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

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

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

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?

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

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the first 12 minutes?

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

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?

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?

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?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

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?