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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 1 m/s²

r_min = m

2.Easy

An 800 kg car drives around a flat curve of radius 60 m at a constant 17 m/s. Find its centripetal acceleration a_c.

m = 800 kgv = 17 m/sr = 60 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 110 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 = 110 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 330 m at 120 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 330 mv = 120 km/hg = 9.81 m/s²

θ = °

5.Hard

A curve of radius 220 m is banked at 25°, 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 = 220 mθ = 25°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

6.Hard

A curve of radius 190 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 190 mθ = 20°μ_s = 0.15g = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 6944 m
2. a_c = 4.817 m/s²
3. v_max = 20.78 m/s
4. θ = 18.94 °
5. v_max = 43.85 m/s
6. v_min = 19.45 m/s

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