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 1600 kg car drives around a flat curve of radius 80 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 27 m/sr = 80 m

F_c = N

2.Easy

A 1.3 kg stone is whirled in a horizontal circle of radius 0.5 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed v_max the stone can have.

m = 1.3 kgr = 0.5 mT_max = 200 N

v_max = m/s

3.Medium

A small ball on a string of length 0.6 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.6 mθ = 50°g = 9.81 m/s²

T = s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 100 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 100 mg = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.5 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 = 0.5 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.9 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 1 mv = 5.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 14580 N
2. v_max = 8.771 m/s
3. T = 1.246 s
4. v_max = 31.32 m/s
5. v_min = 2.215 m/s
6. T = 76.11 N

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