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

A 700 kg car drives around a flat curve of radius 50 m at a constant 26 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 26 m/sr = 50 m

a_c = m/s²

2.Easy

A 900 kg car drives around a flat curve of radius 180 m at a constant 21 m/s. Find the inward (centripetal) force F_c needed.

m = 900 kgv = 21 m/sr = 180 m

F_c = N

3.Medium

A small ball on a string of length 0.6 m moves in a horizontal circle so that the string makes a constant angle of 25° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.6 mθ = 25°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 115 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 115 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg ball on a light string 0.9 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 T_top in the string at the highest point.

m = 2 kgr = 0.9 mv_bottom = 9 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 0.5 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.9 mv = 4.5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 13.52 m/s²
2. F_c = 2205 N
3. v = 1.077 m/s
4. v_max = 21.24 m/s
5. T_top = 81.9 N
6. T = 16.16 N

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