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 15/∘s. What is the linear speed 𝑣 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.

  • A 2.09 in/s, 2.5 rpm, 0.26 rad/s
  • B 2.09 in/s, 2.5 rpm, 0.21 rad/s
  • C 2.09 in/s, 4 rpm, 0.26 rad/s
  • D 3.35 in/s, 2.5 rpm, 0.26 rad/s
  • E 3.35 in/s, 4 rpm, 0.21 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 4800 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.

Q3:

A person is standing on the earth’s equator. Assuming the earth is a sphere with radius 3960 miles, calculate their linear speed in miles per hour correct to two decimal places and their angular speed in radians per hour.

  • A 𝑣 = 1 0 3 6 . 7 3 m p h , πœ” = 0 . 2 6 2 / r a d h
  • B 𝑣 = 1 0 3 6 . 7 3 m p h , πœ” = 0 . 1 / r a d h
  • C 𝑣 = 1 0 3 6 . 7 3 mph, πœ” = 0 . 1 3 / r a d h
  • D 𝑣 = 2 0 7 . 3 5 mph, πœ” = 0 . 2 6 2 / r a d h
  • E 𝑣 = 2 0 7 . 3 5 mph, πœ” = 0 . 0 5 / r a d h

Q4:

A bicycle with 24-inch 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.

  • A 1,320 rad/min, 210.085 rpm
  • B 210.085 rad/min, 1,320 rpm
  • C 1,320 rad/min, 660 rpm
  • D 660 rad/min, 210.085 rpm
  • E 15,840 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 1718.87/∘s
  • Blinear speed = 28 in/s, angular speed = 4.77 rpm or 11718.87/∘s
  • Clinear speed = 28 in/s, angular speed = 4.77 rpm or 28.65/∘s
  • Dlinear speed = 7 in/s, angular speed = 0.08 rpm or 11718.87/∘s
  • Elinear speed = 7 in/s, angular speed = 4.77 rpm or 28.65/∘s

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 disc’s 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:

Emily and her sister were on a circular platform that was spinning around its centre at 12 revolutions per minute. Emily was 5 m from the centre of the platform and her sister was 3.5 m from the centre. Find the speeds π‘†οŒ  and π‘†οŒ‘ at which Emily and her sister, respectively, were moving. Give your answers in metres per second correct to one decimal place.

  • A 𝑆 = 6 . 3  m/s, 𝑆 = 4 . 4  m/s
  • B 𝑆 = 3 . 1  m/s, 𝑆 = 2 . 2  m/s
  • C 𝑆 = 1 2 . 6  m/s, 𝑆 = 8 . 8  m/s
  • D 𝑆 = 3 7 7 . 0  m/s, 𝑆 = 2 6 3 . 9  m/s
  • E 𝑆 = 9 . 4  m/s, 𝑆 = 6 . 6  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 metre per second.

Q11:

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

Q12:

What is the angular speed πœ” 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 π‘Ÿ of the circular path correct to one decimal place.

  • A πœ” = 1 . 2 5 7 / r a d s , π‘Ÿ = 2 2 . 3 m
  • B πœ” = 1 . 2 5 7 / r a d s , π‘Ÿ = 1 1 1 . 4 m
  • C πœ” = 1 . 2 5 7 / r a d s , π‘Ÿ = 3 5 . 2 m
  • D πœ” = 0 . 6 2 8 / r a d s , π‘Ÿ = 1 7 . 6 m
  • E πœ” = 0 . 6 2 8 / r a d s , π‘Ÿ = 4 4 . 6 m

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?

  • A 360 rad/min, 3 9 6 0 rpm
  • B 3 9 6 0 rad/min, 39.375 rpm
  • C 3 9 6 0 rad/min, 630 rpm
  • D 1 9 8 0 rad/min, 39.375 rpm
  • E 1 9 8 0 rad/min, 630 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 disc of radius 61 cm is spinning at 1,269 rpm. Find the speed of a particle on the outer rim, giving your answer in metres 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/s2, find its linear speed, 𝑣, in meters per second and its angular speed, πœ”, in radians per second.

  • A 𝑣 = 8 . 4 9 / m s , πœ” = 0 . 1 3 / r a d s
  • B 𝑣 = 8 . 4 9 / m s , πœ” = 0 . 1 8 / r a d s
  • C 𝑣 = 6 / m s , πœ” = 8 / r a d s
  • D 𝑣 = 6 / m s , πœ” = 0 . 1 8 / r a d s
  • E 𝑣 = 8 / m s , πœ” = 6 / r a d s

Q21:

A hemispherical bowl with a radius of π‘Ÿ meters rests on a table such that its rim is horizontal. If a small ball of mass π‘š kilograms is moving, without friction, along the inside of the bowl in a horizontal circular path whose plane is π‘Ÿ4 meters below the plane of the rim, find the ball’s angular speed in radians per second. Where the acceleration due to gravity is 𝑔 m/s2.

  • A 4 √ π‘Ÿ 𝑔
  • B √ 4 𝑔 π‘Ÿ
  • C ο„ž π‘Ÿ 𝑔 4
  • D √ 4 π‘Ÿ 𝑔
  • E ο„ž 4 𝑔 π‘Ÿ

Q22:

A particle moves in a horizontal circular path with a radius of 175 m at an acceleration of 7 m/s2 towards the centre. Determine its angular speed in radians per second.

Q23:

A hemispherical bowl with a radius of π‘Ÿ rests on a table such that its rim is horizontal. If a small ball of mass π‘š 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 ball’s angular speed. Consider the acceleration due to gravity to be 𝑔.

  • A 3 ο„Ÿ 1 𝑔
  • B √ 2 𝑔 6
  • C √ 𝑔 3
  • D √ 𝑔 9
  • E 3 ο„Ÿ 1 2 𝑔

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