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 m10 m/sF = ?

A 1000 kg car drives around a flat curve of radius 140 m at a constant 10 m/s. Find the inward (centripetal) force Fc needed.

m = 1000 kgv = 10 m/sr = 140 m
Fc = N
2.Easy
r = 0.75 mv = ?90 rpm

A small object sits 75 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find the speed v of the object.

n = 90 rpmr = 0.75 m
v = m/s
3.Medium
r = 145 mvmax​ = ?

A car takes a flat curve of radius 145 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 = 145 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
L = 1.6 m50°

A small ball on a string of length 1.6 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.6 mθ = 50°g = 9.81 m/s²
T = s
5.Hard
R = 9 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 9 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 9 mv₀ = 0
hmin = m
6.Hard
r = 1 m11.5 m/svtop​ = ?

A 1.7 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 11.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.7 kgr = 1 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 714.3 N
  2. 2. v = 7.069 m/s
  3. 3. vmax = 23.85 m/s
  4. 4. T = 2.034 s
  5. 5. hmin = 22.5 m
  6. 6. Ttop = 141.4 N

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