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 = 200 m14 m/sF = ?

A 1100 kg car drives around a flat curve of radius 200 m at a constant 14 m/s. Find the inward (centripetal) force Fc needed.

m = 1100 kgv = 14 m/sr = 200 m
Fc = N
2.Easy
r = 1.9 mvmax​ = ?

A 2 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 30 N. Find the highest speed vmax the stone can have.

m = 2 kgr = 1.9 mTmax = 30 N
vmax = m/s
3.Medium
r = 80 m17 m/s

An 800 kg car drives over the top of a hump in the road at 17 m/s. The top of the hump is a circular arc of radius 80 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 800 kgv = 17 m/sr = 80 mg = 9.81 m/s²
N = N
4.Medium
L = 1.1 m50°

A small ball on a string of length 1.1 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 = 1.1 mθ = 50°g = 9.81 m/s²
T = s
5.Hard
r = 1.2 m11.5 m/svtop​ = ?

A 0.6 kg ball on a light string 1.2 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 = 0.6 kgr = 1.2 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 150 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 150 mθ = 30°μs = 0.3g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. Fc = 1078 N
  2. 2. vmax = 5.339 m/s
  3. 3. N = 4958 N
  4. 4. T = 1.687 s
  5. 5. Ttop = 36.7 N
  6. 6. vmin = 18.65 m/s

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