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 1800 kg car drives around a flat curve of radius 190 m at a constant 21 m/s. Find the inward (centripetal) force F_c needed.

m = 1800 kgv = 21 m/sr = 190 m

F_c = N

2.Easy

A 1400 kg car drives around a flat curve of radius 20 m at a constant 24 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 24 m/sr = 20 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 60 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 = 60 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 135 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 = 135 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 260 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.15. 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 = 260 mθ = 10°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

6.Hard

A 1.1 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 1 mv = 4 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 4178 N
2. a_c = 28.8 m/s²
3. v_max = 13.29 m/s
4. v_max = 25.73 m/s
5. v_max = 29.24 m/s
6. T = 28.39 N

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