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 700 kg car drives around a flat curve of radius 80 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 11 m/sr = 80 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 30 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 65 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 65 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1 mv = 7.5 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 290 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 290 mθ = 12°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 29.98 m/s²
2. a_c = 1.512 m/s²
3. v_max = 14.35 m/s
4. v_max = 19.56 m/s
5. T = 66.06 N
6. v_max = 39.47 m/s

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