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 1600 kg car drives around a flat curve of radius 60 m at a constant 29 m/s. Find its centripetal acceleration a_c.

m = 1600 kgv = 29 m/sr = 60 m

a_c = m/s²

2.Easy

A 1.8 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 90 N. Find the highest speed v_max the stone can have.

m = 1.8 kgr = 1.9 mT_max = 90 N

v_max = m/s

3.Medium

A 1600 kg car drives over the top of a hump in the road at 19 m/s. The top of the hump is a circular arc of radius 120 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1600 kgv = 19 m/sr = 120 mg = 9.81 m/s²

N = N

4.Medium

A curve of radius 360 m is banked at 12°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 360 mθ = 12°g = 9.81 m/s²

v = m/s

5.Hard

A 0.9 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.9 mv = 9 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.7 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 0.7 mv = 8 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 14.02 m/s²
2. v_max = 9.747 m/s
3. N = 10883 N
4. v = 27.4 m/s
5. T = 89.83 N
6. T = 70.87 N

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