Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
r = 70 m26 m/sF = ?

A 1500 kg car drives around a flat curve of radius 70 m at a constant 26 m/s. Find the inward (centripetal) force Fc needed.

m = 1500 kgv = 26 m/sr = 70 m
Fc = N
2.Easy
r = 20 m23 m/sF = ?

A 900 kg car drives around a flat curve of radius 20 m at a constant 23 m/s. Find the inward (centripetal) force Fc needed.

m = 900 kgv = 23 m/sr = 20 m
Fc = N
3.Medium
r = 20 mvmax​ = ?

A car takes a flat curve of radius 20 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 20 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 150 mvmax​ = ?

A car takes a flat curve of radius 150 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 150 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 8°to centrevmax​ = ?

A curve of radius 280 m is banked at 8°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 280 mθ = 8°μs = 0.3g = 9.81 m/s²
vmax = m/s
6.Hard
θ = 15°to centrevmax​ = ?

A curve of radius 120 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 120 mθ = 15°μs = 0.1g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. Fc = 14486 N
  2. 2. Fc = 23805 N
  3. 3. vmax = 10.85 m/s
  4. 4. vmax = 21.01 m/s
  5. 5. vmax = 35.54 m/s
  6. 6. vmax = 21.1 m/s

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