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 small object sits 50 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find the speed v of the object.

n = 30 rpmr = 0.5 m

v = m/s

2.Easy

A 1100 kg car drives around a flat curve of radius 100 m at a constant 16 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 16 m/sr = 100 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 140 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 = 140 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 45 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 = 45 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.5 kg ball on a string 1.2 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 = 1.5 kgr = 1.2 mv = 3.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.3 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 8.5 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 = 0.3 kgr = 1 mv_bottom = 8.5 m/sg = 9.81 m/s²

T_top = N

Answer key

1. v = 1.571 m/s
2. a_c = 2.56 m/s²
3. v_max = 23.44 m/s
4. v_max = 14.86 m/s
5. T = 30.03 N
6. T_top = 6.96 N

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