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 700 kg car drives around a flat curve of radius 110 m at a constant 28 m/s. Find the inward (centripetal) force F_c needed.

m = 700 kgv = 28 m/sr = 110 m

F_c = N

2.Easy

A 600 kg car drives around a flat curve of radius 190 m at a constant 14 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 14 m/sr = 190 m

F_c = N

3.Medium

A car takes a flat curve of radius 60 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 60 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

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 60° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.4 mθ = 60°g = 9.81 m/s²

v = m/s

5.Hard

A curve of radius 90 m is banked at 15°, 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 = 90 mθ = 15°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

6.Hard

A 1.9 kg ball on a string 1.4 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 = 1.4 mv = 5.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 4989 N
2. F_c = 618.9 N
3. v_max = 17.16 m/s
4. v = 2.426 m/s
5. v_max = 20.89 m/s
6. T = 59.69 N

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