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 1.6 kg stone is whirled in a horizontal circle of radius 1.6 m on a smooth, level table, held by a string that breaks at a tension of 100 N. Find the highest speed v_max the stone can have.

m = 1.6 kgr = 1.6 mT_max = 100 N

v_max = m/s

2.Easy

A 1000 kg car drives around a flat curve of radius 180 m at a constant 28 m/s. Find its centripetal acceleration a_c.

m = 1000 kgv = 28 m/sr = 180 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 65 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 = 65 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 135 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 = 135 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.4 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 0.5 mv = 7 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 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 mg = 9.81 m/s²

v_min = m/s

Answer key

1. v_max = 10 m/s
2. a_c = 4.356 m/s²
3. v_max = 15.97 m/s
4. v_max = 32.55 m/s
5. T = 150.9 N
6. v_min = 3.132 m/s

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