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 1200 kg car drives around a flat curve of radius 110 m at a constant 14 m/s. Find the inward (centripetal) force F_c needed.

m = 1200 kgv = 14 m/sr = 110 m

F_c = N

2.Easy

A small object sits 120 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.

n = 33 rpmr = 1.2 m

v = m/s

3.Medium

A car takes a flat curve of radius 125 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 125 mμ_s = 0.8g = 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 80 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 80 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 0.3 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.3 kgr = 1.1 mv_bottom = 11 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 0.9 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.8 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 2138 N
2. v = 4.147 m/s
3. v_max = 31.32 m/s
4. v_max = 28.01 m/s
5. T_top = 18.28 N
6. T = 72.11 N

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