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 700 kg car drives around a flat curve of radius 150 m at a constant 8 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 8 m/sr = 150 m

F_c = N

2.Easy

A 700 kg car drives around a flat curve of radius 160 m at a constant 30 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 30 m/sr = 160 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 75 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 = 75 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 270 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 270 mv = 90 km/hg = 9.81 m/s²

θ = °

5.Hard

A curve of radius 260 m is banked at 8°, 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 = 8°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

6.Hard

A 1.1 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.8 mv = 5.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 298.7 N
2. a_c = 5.625 m/s²
3. v_max = 19.18 m/s
4. θ = 13.28 °
5. v_max = 27.51 m/s
6. T = 52.38 N

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