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 160 m at a constant 18 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 18 m/sr = 160 m

F_c = N

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A small ball on a string of length 1.9 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 time T for one revolution.

L = 1.9 mθ = 30°g = 9.81 m/s²

T = s

4.Medium

A road engineer wants cars to take a curve of radius 170 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 170 mv = 90 km/hg = 9.81 m/s²

θ = °

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 10 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 = 10 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 1.6 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.6 kgr = 0.9 mv = 4 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 1418 N
2. r_min = 3704 m
3. T = 2.573 s
4. θ = 20.54 °
5. T_top = 124.1 N
6. T = 44.14 N

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