Question 1

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?

Accepted Answer

D

Question 2

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

Accepted Answer

E

Question 3

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?

Accepted Answer

The angular acceleration can be calculated using the formula: α = (ω_f - ω_i) / t, where ω_f is the final angular speed, ω_i is the initial angular speed, and t is the time. Substituting the given values: α = (12 rad/s - 8 rad/s) / 4 s = 1.0 rad/s².

Question 4

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?

Accepted Answer

The tangential speed of the tip of a saw tooth can be found using the formula:

v = ωr

where v is the tangential speed, ω is the angular speed, and r is the radius of the blade.

In this case, the radius of the blade is half the diameter, or 0.127 m.

Plugging in the values:

v = (117 rad/s) × 0.127 m 
v = 14.859 m/s

Rounding to the nearest tenth, the answer is:

v ≈ 14.9 m/s

So, the best choice is B.

Question 5

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?

Accepted Answer

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

Question 6

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

Accepted Answer

One radian is equal to the angle at the center of a circle formed by an arc of length equal to the radius. Since the circumference of a circle is 2πr and there are 360 degrees in a full circle, an angle in radians can be converted to degrees using the formula:

angle in degrees = (angle in radians) x (180/π)

In this case, 1.0 radian is equal to:

(1.0) x (180/π) = 57.3°

Therefore, the correct answer is B) 57.3°.

Question 7

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

Accepted Answer

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

Question 8

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?

Accepted Answer

We can use the formula for angular speed (ω) which is given by:

ω = Δθ/Δt

where Δθ is the angular displacement and Δt is the time interval.

In one day, the Earth completes one full rotation, which means the angular displacement is 2π radians. Therefore,

ω = Δθ/Δt = 2π/8.616 × 10^14 s

Simplifying this expression gives:

ω = 7.292 × 10^-5 rad/s

which is approximately equal to 7.292 × 10^1^–15 rad/s in scientific notation. Therefore, the correct answer is A.

Question 9

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?

Accepted Answer

The circular path can be thought of as a part of a circle of radius 30 m. The circumference of this circle is 2πr = 60π m.
The fraction of the circle that the bicycle travels is 141/60π.
The angle in radians that the bicycle travels is equal to the fraction of the circle it travels, i.e., 
θ = (141/60π) × 2π = 4.7 rad (rounded to one decimal place)
Therefore, the answer is D) 4.7 rad.

Question 10

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?

Accepted Answer

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

Question 11

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?

Accepted Answer

The average angular speed is the mean of the initial and final angular speeds: (8.0 rad/s + 12 rad/s) / 2 = 10 rad/s.

Question 12

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?

Accepted Answer

We can use the formula for angular acceleration:

angular acceleration = (change in angular velocity) / time

The change in angular velocity is:

final angular velocity - initial angular velocity 
= 15 rev/s - 35 rev/s 
= -20 rev/s

The time is given as 3.0 s.

So, the angular acceleration is:

angular acceleration = (-20 rev/s) / (3.0 s) 
= -6.7 rev/s^2

Note that the negative sign indicates a decrease in angular velocity, which is consistent with the wheel slowing down. Therefore, the best choice is (C).

Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

We can use the equation for angular acceleration:

angular acceleration = (final angular velocity - initial angular velocity) / time

We are given the initial and final angular velocities, but we need to find the time it takes to slow down. We can use the equation:

Δθ = ω_i t + (1/2)αt^2

where Δθ is the angle turned, ω_i is the initial angular velocity, and α is the angular acceleration. Solving for time, we get:

t = (Δθ - (1/2) ω_i) / (ω_i - ω_f)

Substituting the given values, we get:

t = (180 rad - (1/2)(90 rad/s))(90 rad/s - 30 rad/s)

t = 3 seconds

Now we can use the equation for angular acceleration to find:

angular acceleration = (30 rad/s - 90 rad/s) / 3 s

angular acceleration = -20 rad/s^2

Taking the magnitude of this, we get:

|angular acceleration| = 20 rad/s^2

Therefore, the best choice is D, 20 rad/s^2.

Question 15

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?

Accepted Answer

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

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?

Accepted Answer

The disc made 130 revolutions in 1 minute, so in 31 seconds it made 130 * 31 / 60 = 67 revolutions.

Question 17

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

Accepted Answer

The second hand of a watch completes one full revolution (2π radians) in 60 seconds. Therefore, the angular speed is 2π/60 = 0.10 rad/s.

Question 18

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Question 20

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?

Accepted Answer

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

Quiz 8: Rotational Kinematics