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

m = 700 kgv = 17 m/sr = 90 m

a_c = m/s²

2.Easy

A 1.1 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 20 N. Find the highest speed v_max the stone can have.

m = 1.1 kgr = 1.9 mT_max = 20 N

v_max = m/s

3.Medium

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 95 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 50 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 50 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 1.3 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 1.2 mv = 6.5 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 0.6 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 = 0.6 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 3.211 m/s²
2. v_max = 5.878 m/s
3. v_max = 16.72 m/s
4. v_max = 22.15 m/s
5. T = 58.52 N
6. v_min = 2.426 m/s

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