Question 1

A 0.254-m diameter circular saw blade rotates at a constant angular speed of 117 rad/s.What is the tangential speed of the tip of a saw tooth at the edge of the blade?
A)29.7 m/s
B)14.9 m/s
C)9.46 m/s
D)7.45 m/s
E)2.17 m/s

Accepted Answer

We can use the formula for tangential speed:

v = rω

where v is the tangential speed, r is the radius (which is half the diameter), and ω is the angular speed.

Plugging in the given values, we get:

v = (0.254/2)m × 117 rad/s = 14.9 m/s

Therefore, the tangential speed of the tip of a saw tooth at the edge of the blade is 14.9 m/s, which corresponds to choice (B).

Question 2

Complete the following statement: The angular measure 1.0 radian is equal to
A)0.0175°.
B)57.3°.
C)1.57°.
D)3.14°.
E)6.28°.

Accepted Answer

One radian is equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. The circumference of a circle is 2πr, and there are 360 degrees in a full circle. Therefore, 2π radians is equal to 360 degrees, or 1 radian is equal to 57.3 degrees (approximately).

Question 3

What is the angular speed in rad/s of the second hand of a watch? A)1.7 × 10^-³ rad/s B)0.10 rad/s C)0.02 rad/s D)6.28 rad/s E)60 rad/s

Accepted Answer

B

Question 4

A wheel with a 0.10-m radius is rotating at 35 rev/s.It then slows uniformly to 15 rev/s over a 3.0-s interval.What is the angular acceleration of a point on the wheel? A)-2.0 rev/s² B)0.67 rev/s² C)-6.7 rev/s² D)42 rev/s² E)-17 rev/s²

Accepted Answer

We can use the formula for angular acceleration, which is:

α = (ωf - ωi) / t

where:
ωi = initial angular velocity = 35 rev/s
ωf = final angular velocity = 15 rev/s
t = time interval = 3.0 s

Plugging in the values:

α = (15 rev/s - 35 rev/s) / 3.0 s
α = -20 rev/s / 3.0 s
α = -6.7 rev/s^2

Thus, the angular acceleration of a point on the wheel is -6.7 rev/s^2, which corresponds to choice C.

Question 5

The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles.The actual time is 8.616 × 10⁴ s.Given this information, what is the angular speed of the Earth about its axis? A)7.292 × 10^-⁵ rad/s B)2.321 × 10^-⁶ rad/s C)9.951 × 10^-⁵ rad/s D)6.334 × 10^-⁴ rad/s E)1.990 × 10^-⁷ rad/s

Accepted Answer

To find the angular speed, we need to divide the angle traversed by the time taken.

One revolution of the Earth about its axis corresponds to an angle of 2π radians.

Time taken = 8.616 × 10^4 s

Angular speed = (2π radians) / (8.616 × 10^4 s)

Angular speed = 7.292 × 10^-5 radians per second

So, the answer is choice (A) 7.292 × 10^1-10+5 = 7.292 × 10^5 radians per second.

Question 6

What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation; and the wheel is rotating at 6.53 rev/sec?
A)0.745 m/s
B)1.49 m/s
C)2.98 m/s
D)4.68 m/s
E)9.36 m/s

Accepted Answer

The answer of What is the tangential speed of a...

Question 7

A bicycle travels 141 m along a circular track of radius 30 m.What is the angular displacement in radians of the bicycle from its starting position?
A)1.0 rad
B)1.5 rad
C)3.0 rad
D)4.7 rad
E)9.4 rad

Accepted Answer

The circumference of the circular track is 2πr = 60π m.
To find the angle in radians, we can use the formula:
θ = arc length / radius
θ = 141 / 30
θ ≈ 4.7 radians.

Question 8

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s.The angular speed is then increased to 12 rad/s over the next 4.0 seconds.Assume that the angular acceleration is constant.
-What is the average angular speed of the grindstone?
A)0.5 rad/s
B)2.0 rad/s
C)4.0 rad/s
D)8.0 rad/s
E)10 rad/s

Accepted Answer

The answer of A grindstone of radius 4.0 m is...

Question 9

A 1.0-m roulette wheel reaches a maximum angular speed of 18 rad/s before it begins decelerating.After reaching this maximum angular speed, it turns through 35 revolutions (220 rad) before it stops.How long did it take the wheel to stop after reaching its maximum angular speed?
A)12 s
B)48 s
C)3.7 s
D)8.8 s
E)24 s

Accepted Answer

The answer of A 1.0-m roulette wheel reaches a maximum...

Question 10

A fan rotating with an initial angular velocity of 1000 rev/min is switched off.In 2 seconds, the angular velocity decreases to 200 rev/min.Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?
A)10
B)20
C)100
D)125
E)1200

Accepted Answer

The answer of A fan rotating with an initial angular...

Question 11

A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s.What is its angular acceleration? A)0.313 rad/s² B)0.625 rad/s² C)2.50 rad/s² D)1.97 rad/s² E)3.93 rad/s²

Accepted Answer

The answer of A grindstone, initially at rest, is given...

Question 12

During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev.What is the angular acceleration of the CD? A)358 rad/s² B)126 rad/s² C)901 rad/s² D)866 rad/s² E)794 rad/s²

Accepted Answer

The answer of During the time a compact disc (CD)...

Question 13

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s².What is its angular speed after it has turned through an angle of 628 radians? A)15 rad/s B)19 rad/s C)98 rad/s D)121 rad/s E)150 rad/s

Accepted Answer

The answer of A wheel, originally rotating at 126 rad/s...

Question 14

An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min.If the angular acceleration is constant, how many revolutions does the propeller undergo during this time?
A)7
B)14
C)21
D)49
E)150

Accepted Answer

The answer of An airplane engine starts from rest; and...

Question 15

Through how many revolutions does the grindstone turn during the 4.0-second interval?
A)0.64
B)3.8
C)4.0
D)6.4
E)40

Accepted Answer

The answer of Through how many revolutions does the grindstone...

Question 16

A spinning disc rotating at 130 rev/min slows and stops 31 s later.How many revolutions did the disc make during this time?
A)34
B)67
C)8.4
D)17
E)4.2

Accepted Answer

The answer of A spinning disc rotating at 130 rev/min...

Question 17

Which equation is valid only when the angular measure is expressed in radians?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which equation is valid only when the...

Question 18

A wheel turns through an angle of 188 radians in 8.0 s; and its angular speed at the end of the period is 44 rad/s.If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?
A)3.0 rad/s
B)7.0 rad/s
C)9.1 rad/s
D)23.5 rad/s
E)32.5 rad/s

Accepted Answer

The answer of A wheel turns through an angle of...

Question 19

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s.The angular speed is then increased to 12 rad/s over the next 4.0 seconds.Assume that the angular acceleration is constant. -What is the magnitude of the angular acceleration of the grindstone? A)0.50 rad/s² B)1.0 rad/s² C)4.5 rad/s² D)9.0 rad/s² E)18 rad/s²

Accepted Answer

The answer of A grindstone of radius 4.0 m is...

Question 20

During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians.What is the magnitude of the angular acceleration of the motor? A)64 rad/s² B)32 rad/s² C)10 rad/s² D)20 rad/s² E)1.0 rad/s²

Accepted Answer

We can use the equation:

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

where $\omega_i$ is the initial angular velocity, $\omega_f$ is the final angular velocity, $\alpha$ is the angular acceleration, and $	heta$ is the angle turned.

Substituting the given values, we get:

$(30	ext{ rad/s})^2-(90	ext{ rad/s})^2 = 2\alpha(180	ext{ rad})$

Solving for $\alpha$, we get:

$\alpha = \frac{(30	ext{ rad/s})^2-(90	ext{ rad/s})^2}{2(180	ext{ rad})} = -20	ext{ rad/s}^2$

Note that the negative sign indicates that the angular acceleration is in the opposite direction of the initial angular velocity. The magnitude of the angular acceleration is simply the absolute value of the result, which is:

$|\alpha| = 20	ext{ rad/s}^2$

Thus, the best choice is D.

Quiz 8: Rotational Kinematics

A 0.254-m diameter circular saw blade rotates at a constant angular speed of 117 rad/s.What is the tangential speed of the tip of a saw tooth at the edge of the blade?

Complete the following statement: The angular measure 1.0 radian is equal to

What is the angular speed in rad/s of the second hand of a watch?

A wheel with a 0.10-m radius is rotating at 35 rev/s.It then slows uniformly to 15 rev/s over a 3.0-s interval.What is the angular acceleration of a point on the wheel?

The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles.The actual time is 8.616 × 104 s.Given this information, what is the angular speed of the Earth about its axis?

What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation; and the wheel is rotating at 6.53 rev/sec?

A bicycle travels 141 m along a circular track of radius 30 m.What is the angular displacement in radians of the bicycle from its starting position?

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s.The angular speed is then increased to 12 rad/s over the next 4.0 seconds.Assume that the angular acceleration is constant. -What is the average angular speed of the grindstone?

A 1.0-m roulette wheel reaches a maximum angular speed of 18 rad/s before it begins decelerating.After reaching this maximum angular speed, it turns through 35 revolutions (220 rad) before it stops.How long did it take the wheel to stop after reaching its maximum angular speed?

A fan rotating with an initial angular velocity of 1000 rev/min is switched off.In 2 seconds, the angular velocity decreases to 200 rev/min.Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?

A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s.What is its angular acceleration?

During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev.What is the angular acceleration of the CD?

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s2.What is its angular speed after it has turned through an angle of 628 radians?

An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min.If the angular acceleration is constant, how many revolutions does the propeller undergo during this time?

Through how many revolutions does the grindstone turn during the 4.0-second interval?

A spinning disc rotating at 130 rev/min slows and stops 31 s later.How many revolutions did the disc make during this time?

Which equation is valid only when the angular measure is expressed in radians?

A wheel turns through an angle of 188 radians in 8.0 s; and its angular speed at the end of the period is 44 rad/s.If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s.The angular speed is then increased to 12 rad/s over the next 4.0 seconds.Assume that the angular acceleration is constant. -What is the magnitude of the angular acceleration of the grindstone?

During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians.What is the magnitude of the angular acceleration of the motor?

The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles.The actual time is 8.616 × 10⁴ s.Given this information, what is the angular speed of the Earth about its axis?

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s².What is its angular speed after it has turned through an angle of 628 radians?