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 130 m at a constant 8 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 8 m/sr = 130 m

a_c = m/s²

2.Easy

A 1400 kg car drives around a flat curve of radius 140 m at a constant 15 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 15 m/sr = 140 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 300 m at 120 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 300 mv = 120 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 130 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.6 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.6 kgr = 1 mv = 4.5 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 220 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.25. 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 = 220 mθ = 10°μ_s = 0.25g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 0.4923 m/s²
2. a_c = 1.607 m/s²
3. θ = 20.68 °
4. v_max = 27.66 m/s
5. T = 18.04 N
6. v_max = 31.02 m/s

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