# Worksheet: Angular Speed

In this worksheet, we will practice calculating the angular speed and velocity of a body moving in a circular path.

**Q1: **

A wheel of radius 8 inches is rotating at a rate of . What is the linear speed in inches per second of the wheel, the angular speed in revolutions per minute, and the angular speed in radians per second? Give your answers correct to two decimal places if necessary.

- A2.09 in/s, 4 rpm, 0.26 rad/s
- B3.35 in/s, 2.5 rpm, 0.26 rad/s
- C3.35 in/s, 4 rpm, 0.21 rad/s
- D2.09 in/s, 2.5 rpm, 0.21 rad/s
- E2.09 in/s, 2.5 rpm, 0.26 rad/s

**Q2: **

When burning data to a writable compact disc, the drive adjusts the angular speed in order to keep the linear speed constant where the data is being written. When writing along the outer edge of the disc, the angular speed of a drive is 4,800 rpm (revolutions per minute). Find the linear speed if the CD has a diameter of 120 millimeters. Give your answers in millimeters per minute correct to two decimal places if necessary.

**Q4: **

A bicycle with 24 inches diameter wheels is traveling at 15 mph. Find the angular speed of the wheels in radians per minute (rad/min). How many revolutions per minute (rpm) do the wheels make? Give your answers correct to three decimal places if necessary.

- A660 rad/min, 210.085 rpm
- B210.085 rad/min, 1,320 rpm
- C1,320 rad/min, 210.085 rpm
- D1,320 rad/min, 660 rpm
- E15,840 rad/min, 17.5 rpm

**Q5: **

What is an angular speed of 18.4 rad/s in revolutions per hour? Give your answer correct to one decimal place.

**Q6: **

A wheel of radius 14 inches is rotating at a rate of 0.5 rad/s. What is its linear speed in inches per second, its angular speed in revolutions per minute, and its angular speed in degrees per second? Give your answers correct to two decimal places where necessary.

- Alinear speed = 7 in/s, angular speed = 0.08 rpm or
- Blinear speed = 7 in/s, angular speed = 4.77 rpm or
- Clinear speed = 28 in/s, angular speed = 4.77 rpm or
- Dlinear speed = 7 in/s, angular speed = 0.08 rpm or
- Elinear speed = 28 in/s, angular speed = 4.77 rpm or

**Q7: **

Find the speed of a particle which is moving on a circle of radius 35 m at an angular speed of 8.8 rad/s.

**Q8: **

A CD has diameter of 120 millimeters. When playing audio, a laser and photocell are used to scan data from tracks on the discβs surface, starting near the center and working outward. The angular speed of the disc is gradually reduced as this happens in order to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 rpm (revolutions per minute). Find the linear speed in millimeters per minute, giving your answer correct to two decimal places if necessary.

**Q9: **

Sophia and her sister were on a circular platform that was spinning around its center at 12 revolutions per minute. Sophia was 5 m from the center of the platform and her sister was 3.5 m from the center. Find the speeds and at which Sophia and her sister, respectively, were moving. Give your answers in meters per second correct to one decimal place.

- A m/s, m/s
- B m/s, m/s
- C m/s, m/s
- D m/s, m/s
- E m/s, m/s

**Q10: **

A particle moves in a circular path of radius 6.1 m with an angular speed of 28 rpm. Find the speed of the particle to the nearest tenth of a meter per second.

**Q11: **

A disk of radius 12.5 cm spins at constant angular speed, taking 15 s to complete each revolution. What is the speed of the disk on its outer rim? Give your answer in meters per second correct to four decimal places.

**Q12: **

What is the angular speed of a particle that took 5 seconds to complete a circular path at a constant speed of 28 m/s? Give your answer correct to three decimal places, and use that value to determine the radius of the circular path correct to one decimal place.

- A,
- B,
- C,
- D,
- E,

**Q13: **

A race car is moving at 311 km/h round a circular track of radius 997 m. Determine, correct to three decimal places, its angular speed in radians per second.

**Q14: **

A truck with 32-inch diameter wheels is traveling at 60 mph. Find the angular speed of the wheels in radians per minute. How many revolutions per minute do the wheels make?

- A3,960 rad/min, 630 rpm
- B3,960 rad/min, 39.375 rpm
- C360 rad/min, 3,960 rpm
- D1,980 rad/min, 630 rpm
- E1,980 rad/min, 39.375 rpm

**Q15: **

Express, correct to one decimal place, an angular speed of 117 rpm in radians per second.

**Q16: **

Express an angular speed of 68.1 rad/s in revolutions per minute. Give your answer correct to one decimal place.

**Q17: **

A disk of radius 61 cm is spinning at 1,269 rpm. Find the speed of a particle on the outer rim, giving your answer in meters per second correct to one decimal place.

**Q18: **

A particle is moving in a horizontal circular path at a constant speed of 23 cm/s and a constant angular speed of 32 rpm. Find the radius of the path to the nearest hundredth of a centimetre.

**Q19: **

Determine, in radians per second, the angular speed of a particle that is moving in a circle of radius 4 m at a speed of 6 m/s.

**Q20: **

A particle is moving at constant speed around a horizontal circular path of diameter
1.5 m.
Given that the particle experiences an acceleration of 48 m/s^{2},
find its linear speed, , in meters per second
and its angular
speed, , in radians per second.

- A,
- B,
- C,
- D,
- E,

**Q21: **

A hemispherical bowl with a radius of meters
rests on a table such that its rim is horizontal. If a small ball of mass
kilograms is moving,
without friction, along the inside of the bowl in a horizontal circular path whose plane is
meters below the plane of the rim,
find the ballβs
angular speed in radians per second. Where the acceleration due to gravity is m/s^{2}.

- A
- B
- C
- D
- E

**Q22: **

A particle moves in a horizontal circular path with a radius of
175 m at an acceleration of
7 m/s^{2} toward the center.
Determine its angular speed in radians per second.

**Q23: **

A hemispherical bowl with a radius of rests on a table such that its rim is horizontal. If a small ball of mass is moving, without friction, along the inside of the bowl in a horizontal circular path whose plane is a distance of 9 below the plane of the rim, find the ballβs angular speed. Consider the acceleration due to gravity to be .

- A
- B
- C
- D
- E