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 1.9 kg stone is whirled in a horizontal circle of radius 1.1 m on a smooth, level table, held by a string that breaks at a tension of 120 N. Find the highest speed v_max the stone can have.

m = 1.9 kgr = 1.1 mT_max = 120 N

v_max = m/s

2.Easy

A 600 kg car drives around a flat curve of radius 70 m at a constant 14 m/s. Find its centripetal acceleration a_c.

m = 600 kgv = 14 m/sr = 70 m

a_c = m/s²

3.Medium

An 800 kg car drives over the top of a hump in the road at 13 m/s. The top of the hump is a circular arc of radius 110 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 800 kgv = 13 m/sr = 110 mg = 9.81 m/s²

N = N

4.Medium

A car takes a flat curve of radius 140 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 140 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.5 kg ball on a string 0.5 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 = 0.5 kgr = 0.5 mv = 6.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.7 kg ball on a string 1.5 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 = 1.7 kgr = 1.5 mv = 4 m/sg = 9.81 m/s²

T = N

Answer key

1. v_max = 8.335 m/s
2. a_c = 2.8 m/s²
3. N = 6619 N
4. v_max = 28.71 m/s
5. T = 47.16 N
6. T = 34.81 N

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