Question 1

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 2

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

C

Question 3

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

B

Question 4

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 5

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...

Question 6

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

Accepted Answer

The answer of What is the angular speed about the...

Question 7

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

In the first 20 seconds, the fan rotates 120 revolutions.
In the next 40 seconds, the fan slows down and comes to a stop.
Therefore, in one minute (60 seconds), the fan rotates 120-40 = 80 revolutions.

Therefore, the fan turns through 80 revolutions in one minute.

Question 8

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 9

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 10

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 during a time interval is given by the formula:
average angular acceleration = (final angular velocity - initial angular velocity) / time interval
The instantaneous angular acceleration at any given time is simply the slope of the tangent to the angular velocity vs time graph at that time.
If the wheel undergoes constant angular acceleration, the angular velocity vs time graph will be a straight line, and the instantaneous angular acceleration will be constant.
Therefore, at any time during the period of constant angular acceleration, the instantaneous angular acceleration will be equal to the average angular acceleration over any time interval that includes that time. This means that the answer is all of the above, as all three choices are valid times within the period of constant angular acceleration.

Question 11

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

We can use the equation:

θ = ωi*t + (1/2)*α*t^2

where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time interval.

Plugging in the given values, we get:

θ = (0.500 rad/s)*(7.00 s) + (1/2)*(0.0400 rad/s^2)*(7.00 s)^2
θ = 3.50 rad + 0.980 rad
θ = 4.48 rad

Therefore, the angular displacement is 4.48 rad, which corresponds to choice A.

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

Using the equation:

θ = (1/2)αt²

Where:

θ = final displacement in radians 
α = angular acceleration (given as 2.0 rad/s²) 
t = time interval (given as 5.0 s)

Plugging in the values, we get:

θ = (1/2)(2.0 rad/s²)(5.0 s)² 
θ = 25 rad

Question 13

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

The answer of A fan blade, initially at rest, rotates...

Question 14

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 15

The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length.If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?
A)628 m/s
B)25 m/s
C)19 m/s
D)63 m/s

Accepted Answer

The answer of The end of the cutting cord on...

Question 16

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

The angular acceleration and the angular displacement are given as:

$\alpha = 0.025 \, 	ext{rad/s}^2$
$	heta = 4.2 \, 	ext{rad}$

We can use the following kinematic equation to solve for the final angular speed:

$\omega_f^2 = \omega_i^2 + 2\alpha 	heta$

Since the fan blade is initially at rest, $\omega_i = 0$. Plugging in the given values, we get:

$\omega_f^2 = 2 	imes 0.025 	imes 4.2 = 0.21$

Therefore, the final angular speed is:

$\omega_f = \sqrt{0.21} \approx 0.46 \, 	ext{rad/s}$

So the best choice is (C).

Question 17

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 18

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 19

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 20

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 of each blade tip can be calculated using the formula:
Tangential speed = radius * angular speed
Tangential speed = 0.25m * (20 rev/min) * (2π rad/rev) = 2.5π m/min
Converting to m/s:
Tangential speed = 2.5π m/min * (1 min/60 s) = 0.52 m/s
Therefore, the correct answer is B.

Quiz 7: Rotational Motion and the Law of Gravity

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 0.30-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 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 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?

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

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

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 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 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 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 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.

The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length.If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?

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 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?

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

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

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 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, 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 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 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 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?