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 1500 kg car drives around a flat curve of radius 50 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 11 m/sr = 50 m

a_c = m/s²

2.Easy

A 900 kg car drives around a flat curve of radius 90 m at a constant 17 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 17 m/sr = 90 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 115 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 115 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.4 mμ_s = 0.8g = 9.81 m/s²

n = rpm

5.Hard

A 2 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 0.8 mv = 6 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.9 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.9 mv = 3.5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 2.42 m/s²
2. a_c = 3.211 m/s²
3. v_max = 30.04 m/s
4. n = 21.59 rpm
5. T = 109.6 N
6. T = 21.08 N

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