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 small object sits 135 cm from the axis of a disc that turns at a steady 45 revolutions per minute. Find its centripetal acceleration a_c.

n = 45 rpmr = 1.35 m

a_c = m/s²

2.Easy

A 1800 kg car drives around a flat curve of radius 130 m at a constant 27 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 27 m/sr = 130 m

a_c = m/s²

3.Medium

A 1400 kg car drives over the top of a hump in the road at 12 m/s. The top of the hump is a circular arc of radius 45 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1400 kgv = 12 m/sr = 45 mg = 9.81 m/s²

N = N

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 100 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 100 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 0.6 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.6 kgr = 1.4 mv = 3.5 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 1.3 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1.3 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 29.98 m/s²
2. a_c = 5.608 m/s²
3. N = 9254 N
4. v_max = 31.32 m/s
5. T = 11.14 N
6. v_min = 3.571 m/s

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