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 = 170 m22 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 170 m at a constant 22 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 22 m/sr = 170 m
ac = m/s²
2.Easy
r = 60 m27 m/sF = ?

A 1700 kg car drives around a flat curve of radius 60 m at a constant 27 m/s. Find the inward (centripetal) force Fc needed.

m = 1700 kgv = 27 m/sr = 60 m
Fc = N
3.Medium
r = 3.6 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.6 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.6 mμs = 0.5g = 9.81 m/s²
ω = rad/s
4.Medium
r = 85 mvmax​ = ?

A car takes a flat curve of radius 85 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 85 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.9 mv = 6 m/s

A 1.3 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.9 mv = 6 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.1 m10.5 m/svtop​ = ?

A 0.6 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 10.5 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 = 1.1 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 2.847 m/s²
  2. 2. Fc = 20655 N
  3. 3. ω = 2.335 rad/s
  4. 4. vmax = 18.26 m/s
  5. 5. T = 64.75 N
  6. 6. Ttop = 30.71 N

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