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 60 m at a constant 13 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 13 m/sr = 60 m

a_c = m/s²

2.Easy

A 1000 kg car drives around a flat curve of radius 110 m at a constant 21 m/s. Find the inward (centripetal) force F_c needed.

m = 1000 kgv = 21 m/sr = 110 m

F_c = N

3.Medium

A car takes a flat curve of radius 70 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 = 70 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 60 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 60 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 0.9 mv = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 280 m is banked at 20°, 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 = 280 mθ = 20°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 2.817 m/s²
2. F_c = 4009 N
3. v_max = 21.92 m/s
4. v_max = 17.16 m/s
5. T = 39.62 N
6. v_max = 45.25 m/s

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