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 130 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find the speed v of the object.

n = 78 rpmr = 1.3 m

v = m/s

2.Easy

A 0.1 kg stone is whirled in a horizontal circle of radius 1.7 m on a smooth, level table, held by a string that breaks at a tension of 80 N. Find the highest speed v_max the stone can have.

m = 0.1 kgr = 1.7 mT_max = 80 N

v_max = m/s

3.Medium

A car takes a flat curve of radius 20 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 = 20 mμ_s = 0.5g = 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 85 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 85 mg = 9.81 m/s²

v_max = m/s

5.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

6.Hard

A 1.8 kg ball on a string 0.6 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 = 1.8 kgr = 0.6 mv = 7 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 10.62 m/s
2. v_max = 36.88 m/s
3. v_max = 9.905 m/s
4. v_max = 28.88 m/s
5. v_min = 2.426 m/s
6. T = 164.7 N

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