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 1300 kg car drives around a flat curve of radius 180 m at a constant 14 m/s. Find the inward (centripetal) force F_c needed.

m = 1300 kgv = 14 m/sr = 180 m

F_c = N

2.Easy

A small object sits 15 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find the speed v of the object.

n = 90 rpmr = 0.15 m

v = m/s

3.Medium

A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 100 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 75 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 75 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.4 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 1.1 mv = 6 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 40 m is banked at 30°, 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 = 40 mθ = 30°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 1416 N
2. v = 1.414 m/s
3. v_max = 19.81 m/s
4. v_max = 17.16 m/s
5. T = 59.55 N
6. v_max = 20.41 m/s

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