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 600 kg car drives around a flat curve of radius 130 m at a constant 18 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 18 m/sr = 130 m

F_c = N

2.Easy

A 1.1 kg stone is whirled in a horizontal circle of radius 1.1 m on a smooth, level table, held by a string that breaks at a tension of 130 N. Find the highest speed v_max the stone can have.

m = 1.1 kgr = 1.1 mT_max = 130 N

v_max = m/s

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.4 mμ_s = 0.7g = 9.81 m/s²

n = rpm

4.Medium

A curve of radius 140 m is banked at 10°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 140 mθ = 10°g = 9.81 m/s²

v = m/s

5.Hard

A 0.5 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.5 mv = 6.5 m/sg = 9.81 m/s²

T = 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 3 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 = 3 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 1495 N
2. v_max = 11.4 m/s
3. n = 19.39 rpm
4. v = 15.56 m/s
5. T = 47.16 N
6. T = 31.7 N

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