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 900 kg car drives around a flat curve of radius 130 m at a constant 27 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 27 m/sr = 130 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

v = 250 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A small ball on a string of length 1.5 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.5 mθ = 30°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 75 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 = 75 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.1 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 = 1.1 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.6 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.6 kgr = 0.9 mv_bottom = 10 m/sg = 9.81 m/s²

T_top = N

Answer key

1. a_c = 5.608 m/s²
2. r_min = 3215 m
3. T = 2.286 s
4. v_max = 17.16 m/s
5. v_min = 3.285 m/s
6. T_top = 37.24 N

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