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 = 90 m15 m/sF = ?

A 1000 kg car drives around a flat curve of radius 90 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.

m = 1000 kgv = 15 m/sr = 90 m
Fc = N
2.Easy
r = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 1.2 m/s²
rmin = m
3.Medium
r = 70 mvmax​ = ?

A car takes a flat curve of radius 70 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 70 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
θ = ?to centre50 km/h

A road engineer wants cars to take a curve of radius 160 m at 50 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 160 mv = 50 km/hg = 9.81 m/s²
θ = °
5.Hard
R = 5 mh = 20 m

A 5 kg cart is released from rest at a height of 20 m on a frictionless track and runs through a vertical loop of radius 5 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 5 kgh = 20 mR = 5 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 0.6 m7.5 m/svtop​ = ?

A 0.6 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 7.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.6 kgr = 0.6 mvbottom = 7.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 2500 N
  2. 2. rmin = 3704 m
  3. 3. vmax = 23.44 m/s
  4. 4. θ = 7.006 °
  5. 5. Nbottom = 441.5 N
  6. 6. Ttop = 26.82 N

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