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 145 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find the speed v of the object.

n = 120 rpmr = 1.45 m

v = m/s

2.Easy

A 0.3 kg stone is whirled in a horizontal circle of radius 0.4 m on a smooth, level table, held by a string that breaks at a tension of 130 N. Find the highest speed v_max the stone can have.

m = 0.3 kgr = 0.4 mT_max = 130 N

v_max = m/s

3.Medium

An 800 kg car drives over the top of a hump in the road at 14 m/s. The top of the hump is a circular arc of radius 65 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 800 kgv = 14 m/sr = 65 mg = 9.81 m/s²

N = N

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 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 0.8 kg ball on a string 1.3 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 = 0.8 kgr = 1.3 mv = 6.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 18.22 m/s
2. v_max = 13.17 m/s
3. N = 5436 N
4. v_max = 14.86 m/s
5. v_min = 2.426 m/s
6. T = 33.85 N

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