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 900 kg car drives around a flat curve of radius 90 m at a constant 19 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 19 m/sr = 90 m

a_c = m/s²

2.Easy

A 700 kg car drives around a flat curve of radius 110 m at a constant 23 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 23 m/sr = 110 m

F_c = N

3.Medium

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 105 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A curve of radius 210 m is banked at 25°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 210 mθ = 25°g = 9.81 m/s²

v = m/s

5.Hard

A 1.1 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 1.4 mv = 5 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 1.5 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 = 1.5 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 4.011 m/s²
2. F_c = 3366 N
3. v_max = 28.71 m/s
4. v = 30.99 m/s
5. T = 30.43 N
6. v_min = 3.836 m/s

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