Question 1

An artificial satellite in a low orbit circles the earth every 98 minutes.What is its angular speed in rad/s?

Accepted Answer

The answer of An artificial satellite in a low orbit...

Question 2

A child is riding a merry-go-round that is turning at 7.18 rpm.If the child is standing 4.65 m from the center of the merry-go-round,how fast is the child moving?
A)5.64 m/s
B)3.50 m/s
C)0.556 m/s
D)1.75 m/s
E)1.80 m/s

Accepted Answer

We can use the formula for linear velocity on a rotating object:

v = rw

where v is the linear velocity, r is the radius, and w is the angular velocity.

First, we need to convert the angular velocity from rpm to radians per second:

w = 7.18 rpm * (2π radians/1 revolution) * (1 minute/60 seconds) = 0.75 radians/second

Then we can plug in the values:

v = (4.65 m) * (0.75 radians/second) = 3.4875 m/s

Rounding to two significant figures, we get:

v ≈ 3.5 m/s

Therefore, the best choice is B.

Question 3

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m.What is the magnitude of its angular acceleration if there was no slipping? A)1.8 rad/s² B)0.90 rad/s² C)5.7 rad/s² D)11 rad/s²

Accepted Answer

The angular acceleration can be found using the relation between linear acceleration and angular acceleration, $a = \alpha r$, where $a$ is the linear acceleration, $\alpha$ is the angular acceleration, and $r$ is the radius of the wheel. First, we find the linear acceleration using the equation $v^2 = u^2 + 2as$, where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $s$ is the distance. Given that the wheel comes to rest, $v = 0$, $u = 8.4$ m/s (initial velocity), and $s = 115$ m, we can solve for $a$. Then, using the radius $r = \frac{68}{2} = 34$ cm $= 0.34$ m, we can find $\alpha$.Solving for $a$, we have $0 = (8.4)^2 + 2a(115)$, which gives $a = -\frac{(8.4)^2}{2 \times 115}$. Plugging in the values, we find $a \approx -0.303$ m/s$^2$. Then, using $a = \alpha r$, we get $\alpha = \frac{a}{r} = \frac{-0.303}{0.34}$, which gives $\alpha \approx -0.90$ rad/s$^2$. The negative sign indicates deceleration, but since the question asks for the magnitude, we take the absolute value, which is $0.90$ rad/s$^2$.

Question 4

A wheel of diameter 0.70 m rolls on the floor without slipping.A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor.
(a)At what speed is the central axis of the wheel moving relative to the floor?
(b)What is the angular speed of the wheel?

Accepted Answer

The answer of A wheel of diameter 0.70 m rolls...

Question 5

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?
A)11 rad/s
B)22 rad/s
C)45 rad/s
D)69 rad/s
E)660 rad/s

Accepted Answer

To convert revolutions per minute (rpm) to radians per second (rad/s), use the conversion factor $2\pi$ rad/rev and the fact that there are 60 seconds in a minute. Thus, $210 \, \text{rpm} = 210 \times \frac{2\pi}{60} \, \text{rad/s} = 22 \, \text{rad/s}$.

Question 6

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s.
(a)Through what angle does the bowling ball turn as it travels the length of the lane?
(b)What is the angular speed of the bowling ball?
(c)Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have.
(d)Calculate the tangential acceleration of a point on the surface of the bowling ball.

Accepted Answer

The answer of A bowling ball of mass 7.5 kg...

Question 7

Through how many degrees does a 33 rpm turntable rotate in $0.32 \text { s? }$
A)63°
B)35°
C)46°
D)74°

Accepted Answer

A 33 rpm turntable rotates at 33 revolutions per minute, which is 33/60 revolutions per second. In 0.32 seconds, it completes (33/60) * 0.32 revolutions. Each revolution is 360 degrees, so the total rotation is (33/60) * 0.32 * 360 = 63.36 degrees, approximately 63°.

Question 8

The diameter of the Moon is 3.47 × 10⁶ m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

Accepted Answer

The answer of The diameter of the Moon is 3.47...

Question 9

A bicycle has wheels that are 60 cm in diameter.What is the angular speed of these wheels when it is moving at 4.0 m/s?
A)1.2 rad/s
B)4.8 rad/s
C)0.36 rad/s
D)13 rad/s
E)7.6 rad/s

Accepted Answer

The answer of A bicycle has wheels that are 60...

Question 10

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Accepted Answer

The answer of Express the angular speed of an old...

Question 11

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping.Through how many degrees does the cylinder turn during this time?

Accepted Answer

The answer of A cylinder of radius 8.0 cm rolls...

Question 12

When Mary is 3.00 m from the center of a merry-go-round,her tangential speed is a constant 1.88 m/s.
(a)What is her angular speed in rad/s?
(b)What is the magnitude of her linear acceleration?

Accepted Answer

The answer of When Mary is 3.00 m from the...

Question 13

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?
A)47.7 rpm
B)955 rpm
C)72.0 rpm
D)50.0 rpm
E)100 rpm

Accepted Answer

The angular speed (ω) can be calculated using the formula ω = v/r, where v is the linear speed and r is the radius of the wheel. Given the diameter is 120 mm (or 0.12 m), the radius is 0.06 m. With a speed of 6.00 m/s, ω = 6.00 / 0.06 = 100 rad/s. To convert to revolutions per minute (rpm), use the conversion factor 1 rad/s = 9.5493 rpm, so 100 rad/s * 9.5493 = 955 rpm.

Question 14

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?
A)4.13 s
B)2.07 s
C)118 s
D)4.77 s
E)8.26 s

Accepted Answer

The time to complete one revolution is given by $T = \frac{2\pi}{\omega}$, where $\omega$ is the angular speed. Substituting $\omega = 1.52 \, \text{rad/s}$, we get $T = \frac{2\pi}{1.52} \approx 4.13 \, \text{s}$.

Question 15

A bicycle wheel has an outside diameter of 66 cm.Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

Accepted Answer

The answer of A bicycle wheel has an outside diameter...

Question 16

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?
A)100 rad/s
B)50 rad/s
C)25 rad/s
D)20 rad/s
E)10 rad/s

Accepted Answer

The angular speed, $\omega$, can be found using the relationship $\omega = v/r$, where $v$ is the linear speed of the string and $r$ is the radius of the pulley. Given $v = 5.0 \, \text{m/s}$ and $r = 5.0 \, \text{cm} = 0.05 \, \text{m}$, $\omega = 5.0 \, \text{m/s} / 0.05 \, \text{m} = 100 \, \text{rad/s}$.

Question 17

An electrical motor spins at a constant $2695.0 \mathrm { rpm }$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor? A)5707 m/s² B)281.6 m/s² C)572,400 m/s² D)28.20 m/s²

Accepted Answer

The linear acceleration $a$ of the edge of the rotor can be calculated using the formula $a = r\omega^2$, where $r$ is the radius of the rotor and $\omega$ is the angular velocity in radians per second. First, convert the rotational speed from rpm to rad/s: $\omega = 2695.0 \times \frac{2\pi}{60} \approx 282.743 \, \text{rad/s}$. Then, with $r = 7.165 \, \text{cm} = 0.07165 \, \text{m}$, the linear acceleration is $a = 0.07165 \times (282.743)^2 \approx 5707 \, \text{m/s}^2$.

Question 18

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?
A)85.14 rad/s
B)13.53 rad/s
C)63.84 rad/s
D)95.33 rad/s

Accepted Answer

Angular speed is measured in radians per second (rad/s). To convert from revolutions per minute (rpm) to radians per second, we use the conversion factor:
1 rpm = (2π/60) rad/s
where 2π is the number of radians in one revolution, divided by 60 seconds per minute. 
So, angular speed (ω) in radians per second is given by:
ω = (2π/60) × rpm
ω = (2π/60) × 813.0 rpm 
ω = 85.14 rad/s (rounded to two decimal places)

Question 19

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan? A)0.86 rad/s² B)0.74 rad/s² C)0.37 rad/s² D)11 rad/s² E)1.2 rad/s²

Accepted Answer

The answer of When a fan is turned off,its angular...

Question 20

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth,and its distance from Earth is 1.5 × 10¹¹m.What is the diameter of the sun?

Accepted Answer

The answer of The sun subtends an angle of 0.00928...

Quiz 9: Rotational Motion

An artificial satellite in a low orbit circles the earth every 98 minutes.What is its angular speed in rad/s?

A child is riding a merry-go-round that is turning at 7.18 rpm.If the child is standing 4.65 m from the center of the merry-go-round,how fast is the child moving?

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m.What is the magnitude of its angular acceleration if there was no slipping?

A wheel of diameter 0.70 m rolls on the floor without slipping.A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a)At what speed is the central axis of the wheel moving relative to the floor? (b)What is the angular speed of the wheel?

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

Through how many degrees does a 33 rpm turntable rotate in 0.32 s? 0.32 \text { s? }0.32 s?

The diameter of the Moon is 3.47 × 106 m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

A bicycle has wheels that are 60 cm in diameter.What is the angular speed of these wheels when it is moving at 4.0 m/s?

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping.Through how many degrees does the cylinder turn during this time?

When Mary is 3.00 m from the center of a merry-go-round,her tangential speed is a constant 1.88 m/s. (a)What is her angular speed in rad/s? (b)What is the magnitude of her linear acceleration?

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?

A bicycle wheel has an outside diameter of 66 cm.Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

An electrical motor spins at a constant 2695.0rpm2695.0 \mathrm { rpm }2695.0rpm If the rotor radius is 7.165 cm7.165 \mathrm {~cm}7.165 cm what is the linear acceleration of the edge of the rotor?

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan?

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth,and its distance from Earth is 1.5 × 1011 m.What is the diameter of the sun?

Through how many degrees does a 33 rpm turntable rotate in $0.32 \text { s? }$

The diameter of the Moon is 3.47 × 10⁶ m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

An electrical motor spins at a constant $2695.0 \mathrm { rpm }$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor?

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth,and its distance from Earth is 1.5 × 10¹¹m.What is the diameter of the sun?