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 1400 kg car drives around a flat curve of radius 160 m at a constant 16 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 16 m/sr = 160 m

F_c = N

2.Easy

A 1800 kg car drives around a flat curve of radius 160 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 9 m/sr = 160 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 145 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 = 145 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 115 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 115 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg ball on a string 1 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 = 2 kgr = 1 mv = 5 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.3 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 7.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.3 kgr = 0.6 mv_bottom = 7.5 m/sg = 9.81 m/s²

T_top = N

Answer key

1. F_c = 2240 N
2. a_c = 0.5062 m/s²
3. v_max = 31.55 m/s
4. v_max = 33.59 m/s
5. T = 69.62 N
6. T_top = 13.41 N

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