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 = 60 m8 m/sF = ?

A 1800 kg car drives around a flat curve of radius 60 m at a constant 8 m/s. Find the inward (centripetal) force Fc needed.

m = 1800 kgv = 8 m/sr = 60 m
Fc = N
2.Easy
r = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 2 m/s²
rmin = m
3.Medium
r = 4 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 4 mμs = 0.6g = 9.81 m/s²
ω = rad/s
4.Medium
r = 110 m5 m/s

A 1400 kg car drives over the top of a hump in the road at 5 m/s. The top of the hump is a circular arc of radius 110 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1400 kgv = 5 m/sr = 110 mg = 9.81 m/s²
N = N
5.Hard
r = 0.5 m9 m/svtop​ = ?

A 1.8 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.8 kgr = 0.5 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.5 m9.5 m/svtop​ = ?

A 0.8 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 9.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.8 kgr = 0.5 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 1920 N
  2. 2. rmin = 2222 m
  3. 3. ω = 2.022 rad/s
  4. 4. N = 13416 N
  5. 5. Ttop = 203.3 N
  6. 6. Ttop = 105.2 N

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