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 600 kg car drives around a flat curve of radius 160 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 27 m/sr = 160 m

F_c = N

2.Easy

A 1500 kg car drives around a flat curve of radius 130 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 1500 kgv = 27 m/sr = 130 m

F_c = N

3.Medium

A 1500 kg car drives over the top of a hump in the road at 6 m/s. The top of the hump is a circular arc of radius 85 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1500 kgv = 6 m/sr = 85 mg = 9.81 m/s²

N = N

4.Medium

A small ball on a string of length 0.4 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.4 mθ = 45°g = 9.81 m/s²

T = s

5.Hard

A 0.9 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.9 kgr = 0.7 mv = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 260 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.2. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 260 mθ = 10°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 2734 N
2. F_c = 8412 N
3. N = 14080 N
4. T = 1.067 s
5. T = 20.4 N
6. v_max = 31.54 m/s

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