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 0.8 kg stone is whirled in a horizontal circle of radius 1.5 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 = 0.8 kgr = 1.5 mT_max = 90 N

v_max = m/s

2.Easy

A 1400 kg car drives around a flat curve of radius 100 m at a constant 13 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 13 m/sr = 100 m

F_c = N

3.Medium

A car takes a flat curve of radius 25 m. 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 the car can take the curve without skidding.

r = 25 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A curve of radius 240 m is banked at 18°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 240 mθ = 18°g = 9.81 m/s²

v = m/s

5.Hard

A curve of radius 120 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 120 mθ = 12°μ_s = 0.15g = 9.81 m/s²

v_min = m/s

6.Hard

A 1.3 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 = 1.3 kgr = 1.4 mv = 5 m/sg = 9.81 m/s²

T = N

Answer key

1. v_max = 12.99 m/s
2. F_c = 2366 N
3. v_max = 8.578 m/s
4. v = 27.66 m/s
5. v_min = 8.448 m/s
6. T = 35.97 N

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