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 1.8 kg stone is whirled in a horizontal circle of radius 0.6 m on a smooth, level table, held by a string that breaks at a tension of 90 N. Find the highest speed v_max the stone can have.

m = 1.8 kgr = 0.6 mT_max = 90 N

v_max = m/s

2.Easy

A 1500 kg car drives around a flat curve of radius 60 m at a constant 15 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 15 m/sr = 60 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 100 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 = 100 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 150 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 = 150 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.2 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 0.7 mv = 4 m/sg = 9.81 m/s²

T = N

Answer key

1. v_max = 5.477 m/s
2. a_c = 3.75 m/s²
3. v_max = 22.15 m/s
4. v_max = 27.12 m/s
5. v_min = 2.62 m/s
6. T = 39.2 N

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