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 1100 kg car drives around a flat curve of radius 200 m at a constant 27 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 27 m/sr = 200 m

a_c = m/s²

2.Easy

A 1.8 kg stone is whirled in a horizontal circle of radius 0.3 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 = 1.8 kgr = 0.3 mT_max = 120 N

v_max = m/s

3.Medium

A small ball on a string of length 1.1 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.1 mθ = 40°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 105 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 = 105 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.3 kg ball on a string 1.4 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 = 0.3 kgr = 1.4 mv = 4 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 3.645 m/s²
2. v_max = 4.472 m/s
3. T = 1.841 s
4. v_max = 17.58 m/s
5. T = 6.372 N
6. v_min = 3.571 m/s

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