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 1.2 m/s². What is the smallest radius r_min for a curve taken at 200 km/h?

v = 200 km/ha_max = 1.2 m/s²

r_min = m

2.Easy

A 700 kg car drives around a flat curve of radius 50 m at a constant 25 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 25 m/sr = 50 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 135 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 = 135 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 30 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 = 30 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.3 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1.3 mg = 9.81 m/s²

v_min = m/s

6.Hard

A curve of radius 160 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 = 160 mθ = 8°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

Answer key

1. r_min = 2572 m
2. a_c = 12.5 m/s²
3. v_max = 23.02 m/s
4. v_max = 12.13 m/s
5. v_min = 3.571 m/s
6. v_max = 21.58 m/s

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