Question 1

What is the angular speed about the rotational axis of the Earth for a person standing on the surface? A)7.3 x 10^-5rad/s B)3.6 x10^-5 rad/s C)6.28 x 10^-5rad/s D)3.14 x 10^-5rad/s

Accepted Answer

A

Question 2

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is the time interval required for it to reach a 4.2-rad displacement after starting from rest? A)1.8 s B)2.0 s C)16 s D)18 s

Accepted Answer

D

Question 3

A ventilation fan has blades 0.25 m in radius rotating at 20 rpm.What is the tangential speed of each blade tip?
A)0.02 m/s
B)0.52 m/s
C)5.0 m/s
D)20 m/s

Accepted Answer

The tangential speed can be calculated using the formula:
tangential speed = radius x angular speed
tangential speed = 0.25m x 2π x (20/60) Hz
tangential speed ≈ 0.52 m/s. 
Therefore, the correct answer is B) 0.52 m/s.

Question 4

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration? A)9.6 rad/s² B)4.8 rad/s² C)1.6 rad/s² D)0.33 rad/s²

Accepted Answer

The answer of A 0.12-m-radius grinding wheel takes 5.5 s...

Question 5

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s² over a 5.0-s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5-s interval? A)33 m/s² B)6.7 m/s² C)0.60 m/s² D)0.30 m/s²

Accepted Answer

The answer of A 0.30-m-radius automobile tire accelerates from rest...

Question 6

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is its angular speed at the instant it goes through an angular displacement of 4.2 rad? A)0.025 rad/s B)0.11 rad/s C)0.46 rad/s D)1.2 rad/s

Accepted Answer

Using the equation: 
θ = initial angular speed × t + 1/2 × angular acceleration × t²

We can find the time it takes for the blade to rotate through 4.2 rad:

4.2 rad = 0 × t + 1/2 × 0.025 rad/s² × t² 
t = √(4.2 rad / (1/2 × 0.025 rad/s²)) 
t = 8.16 s

Then the final angular speed can be found using:

final angular speed = initial angular speed + angular acceleration × time

final angular speed = 0 + 0.025 rad/s² × 8.16 s 
final angular speed = 0.204 rad/s

Therefore, the best choice is C: 0.46 rad/s.

Question 7

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?
A)0.25 T
B)0.50 T
C)0.67 T
D)0.71 T

Accepted Answer

The wheel reaches its average angular speed at 0.50T because the average angular speed is defined as the total angular displacement divided by the total time, which, under constant acceleration, is reached at the midpoint of the time interval.

Question 8

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?
A)3.2 rad/s
B)26 rad/s
C)52 rad/s
D)81 rad/s

Accepted Answer

To convert from revolutions per second to radians per second, we need to multiply by 2π, since there are 2π radians in one revolution. Thus, the angular speed of the grindstone is approximately 8.3 x 2π = 52 rad/s. Therefore, the answer is choice C.

Question 9

A 0.15-m-radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s.What is the average tangential acceleration of a point on the wheel's edge? A)0.45 m/s² B)6.8 m/s² C)28 m/s² D)14 m/s²

Accepted Answer

The answer of A 0.15-m-radius grinding wheel starts at rest...

Question 10

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 40 s.The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?
A)2
B)0.5
C)-0.5
D)-2

Accepted Answer

The answer of A ceiling fan is turned on and...

Question 11

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?
A)20
B)60
C)0
D)600

Accepted Answer

First, we need to find the total number of revolutions the fan makes while it is on. We can use the formula:

angular speed = (change in angle) / time

where the change in angle is measured in radians and the time is in seconds. We know the angular speed (120 rev/min), and we can convert it to radians/second:

120 rev/min = (120 rev/min) * (2π rad/rev) * (1/60 min/s) = 4π rad/s

We also know the time (20 s), so we can solve for the change in angle:

4π rad/s = (change in angle) / 20 s

(change in angle) = 80π rad

To find the number of revolutions, we divide the change in angle by 2π:

number of revolutions = (80π rad) / (2π rad/rev) = 40 rev

So the fan turns 40 revolutions while it is on.

Next, we need to find how many revolutions the fan makes as it is coasting to a stop. When the fan is turned off, there are no external forces acting on it, so the total angular momentum is conserved. This means that the fan will continue to spin at the same angular speed, but with a decreasing frequency until it comes to a stop.

We can use the formula:

angular speed = (change in angle) / time

to find the angular speed at any point in time. We know that the initial angular speed is 4π rad/s (from when the fan is turned off), and we know that it comes to a stop in 40 s. So, after t seconds of coasting, the angular speed will be:

4π rad/s = (change in angle) / t

(change in angle) = 4πt

To find the total number of revolutions during the 40 s of coasting, we integrate the angular speed with respect to time from t=0 to t=40:

number of revolutions = ∫(4πt) dt from 0 to 40
= [2πt^2] from 0 to 40
= 3200π / (2π)
= 1600 rev

So the fan turns 1600 revolutions while it is coasting to a stop.

Therefore, the total number of revolutions during the one minute of rotation is:

40 + 1600 = 1640

The best choice is B, that is, the fan makes 60 revolutions.

Question 12

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 5.0-s interval? A)12.5 rad B)25 rad C)2.0 rad D)0.50 rad

Accepted Answer

The angular velocity of the tire increases at a constant rate of 2.0 rad/s^2, so we can use the kinematic equation:
θ = ωi t + ½ α t^2
where
θ = final angle
ωi = initial angular velocity = 0 rad/s (starting from rest)
α = angular acceleration = 2.0 rad/s^2
t = time interval = 5.0 s

Plugging in the values, we get:
θ = 0 + ½ (2.0 rad/s^2) (5.0 s)^2
θ = 25 rad

Therefore, the tire rotates 25 radians during the 5.0 second interval. Answer B is the best choice.

Question 13

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?
A)0.50 T
B)0.67 T
C)0.71 T
D)all of the above

Accepted Answer

The average angular acceleration for a constant angular acceleration is half of the instantaneous angular acceleration. Therefore, the average angular acceleration will be equal to the instantaneous angular acceleration at half the time, which is 0.50T. Additionally, since the angular acceleration is constant, the instantaneous angular acceleration will remain the same throughout the motion. Therefore, the answer is all of the above as the average and instantaneous angular acceleration will be equal at 0.50T, 0.67T, and 0.71T.

Question 14

2 600 rev/min is equivalent to which of the following?
A)2600 rad/s
B)43.3 rad/s
C)273 rad/s
D)60 rad/s

Accepted Answer

The answer of 2 600 rev/min is equivalent to which...

Question 15

Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 20.0 seconds have elapsed.How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 20.0 second interval?
A)10.0 s
B)12.4 s
C)14.2 s
D)15.0 s

Accepted Answer

We can use the kinematic equation for angular displacement:

θ = ω_i*t + (1/2)*alpha*t^2

where θ is the angular displacement, ω_i is the initial angular velocity, alpha is the angular acceleration, and t is time.

We know that the final angular velocity is 30.0 rad/s, and that the initial angular velocity is 10.0 rad/s. We also know that the time elapsed is 20.0 s. Using these values, we can solve for alpha:

30.0 rad/s = 10.0 rad/s + alpha*(20.0 s)
alpha = 1.0 rad/s^2

Now we want to find the time it takes for the wheel to undergo half of its total angular displacement during the 20.0 second interval. We can find the total angular displacement using the same kinematic equation:

θ = ω_i*t + (1/2)*alpha*t^2

θ = 10.0 rad/s * 20.0 s + (1/2)*1.0 rad/s^2 * (20.0 s)^2 
θ = 200.0 rad

So we want to find the time it takes for the wheel to undergo 100.0 rad of angular displacement. Rearranging the kinematic equation to solve for time, we get:

t = (-ω_i ± sqrt(ω_i^2 + 2*alpha*θ))/alpha

Using the positive root, we get:

t = (-10.0 rad/s ± sqrt((10.0 rad/s)^2 + 2*(1.0 rad/s^2)*(100.0 rad)))/(1.0 rad/s^2)

t = (-10.0 rad/s ± 40.0 s)/1.0 rad/s^2

The positive time value is:

t = (-10.0 rad/s + 40.0 s)/1.0 rad/s^2 = 30.0 s

So it takes 30.0 seconds for the wheel to undergo half of its total angular displacement during the 20.0 second interval. However, we are looking for the time after the initial time (t = 0), so we need to subtract the initial time from this value:

t_half = 30.0 s - 0 s = 30.0 s

Therefore, the correct answer is not listed, and the problem may contain an error.

Question 16

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s².What angular displacement does the Ferris wheel undergo in this 7-s interval? A)4.48 rad B)2.50 rad C)3.00 rad D)0.500 rad

Accepted Answer

The answer of A Ferris wheel,rotating initially at an angular...

Question 17

A spool of thread has an average radius of 1.00 cm.If the spool contains 62.8 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.
A)100
B)1 000
C)3 140
D)62 800

Accepted Answer

The answer of A spool of thread has an average...

Question 18

A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 m/s.What is the tangential speed of a point 0.20 m from the center of the same wheel?
A)1.0 m/s
B)1.3 m/s
C)2.7 m/s
D)8.0 m/s

Accepted Answer

The answer of A point on the rim of a...

Question 19

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 7.0-s interval at a rate of 0.040 rad/s².What is its angular speed after this 7-s interval? A)0.20 rad/s B)0.30 rad/s C)0.46 rad/s D)0.78 rad/s

Accepted Answer

The answer of A Ferris wheel,rotating initially at an angular...

Question 20

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration? A)0.10 rad/s² B)0.05 rad/s² C)1.8 rad/s² D)0.60 rad/s²

Accepted Answer

The answer of A Ferris wheel starts at rest and...

Quiz 7: Rotational Motion and the Law of Gravity

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s2.What is the time interval required for it to reach a 4.2-rad displacement after starting from rest?

A ventilation fan has blades 0.25 m in radius rotating at 20 rpm.What is the tangential speed of each blade tip?

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s2 over a 5.0-s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5-s interval?

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s2.What is its angular speed at the instant it goes through an angular displacement of 4.2 rad?

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?

A 0.15-m-radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s.What is the average tangential acceleration of a point on the wheel's edge?

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 40 s.The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 5.0-s interval?

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?

2 600 rev/min is equivalent to which of the following?

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s2.What angular displacement does the Ferris wheel undergo in this 7-s interval?

A spool of thread has an average radius of 1.00 cm.If the spool contains 62.8 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 m/s.What is the tangential speed of a point 0.20 m from the center of the same wheel?

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 7.0-s interval at a rate of 0.040 rad/s2.What is its angular speed after this 7-s interval?

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration?

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is the time interval required for it to reach a 4.2-rad displacement after starting from rest?

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s² over a 5.0-s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5-s interval?

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is its angular speed at the instant it goes through an angular displacement of 4.2 rad?

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 5.0-s interval?

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s².What angular displacement does the Ferris wheel undergo in this 7-s interval?

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 7.0-s interval at a rate of 0.040 rad/s².What is its angular speed after this 7-s interval?