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 = 140 m15 m/sF = ?

A 900 kg car drives around a flat curve of radius 140 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.

m = 900 kgv = 15 m/sr = 140 m
Fc = N
2.Easy
r = 1.4 mv = ?200 rpm

A small object sits 140 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find the speed v of the object.

n = 200 rpmr = 1.4 m
v = m/s
3.Medium
r = 3.7 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.7 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
L = 1.4 m30°

A small ball on a string of length 1.4 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.4 mθ = 30°g = 9.81 m/s²
v = m/s
5.Hard
θ = 18°to centrevmax​ = ?

A curve of radius 270 m is banked at 18°, and the coefficient of static friction between tyres and road is 0.2. 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 = 270 mθ = 18°μs = 0.2g = 9.81 m/s²
vmax = m/s
6.Hard
r = 1.2 m8 m/svtop​ = ?

A 1.3 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 8 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.3 kgr = 1.2 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 1446 N
  2. 2. v = 29.32 m/s
  3. 3. n = 28.39 rpm
  4. 4. v = 1.991 m/s
  5. 5. vmax = 38.56 m/s
  6. 6. Ttop = 5.568 N

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