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 180 m at a constant 30 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 30 m/sr = 180 m

F_c = N

2.Easy

An 800 kg car drives around a flat curve of radius 50 m at a constant 30 m/s. Find the inward (centripetal) force F_c needed.

m = 800 kgv = 30 m/sr = 50 m

F_c = N

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 35° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.1 mθ = 35°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 60 m. The coefficient of static friction between tyres and road is 0.6. 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 = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.4 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 1.4 mv = 3.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.7 kg ball on a string 1.5 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 = 1.7 kgr = 1.5 mv = 5.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 8000 N
2. F_c = 14400 N
3. v = 2.082 m/s
4. v_max = 18.79 m/s
5. T = 25.98 N
6. T = 50.96 N

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