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 90 m at a constant 15 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 15 m/sr = 90 m

F_c = N

2.Easy

A 1100 kg car drives around a flat curve of radius 100 m at a constant 28 m/s. Find the inward (centripetal) force F_c needed.

m = 1100 kgv = 28 m/sr = 100 m

F_c = N

3.Medium

A car takes a flat curve of radius 115 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 = 115 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A small ball on a string of length 1.3 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 speed v of the ball.

L = 1.3 mθ = 50°g = 9.81 m/s²

v = m/s

5.Hard

A 0.8 kg ball on a string 0.5 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 = 0.8 kgr = 0.5 mv = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 110 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 = 110 mθ = 15°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 4000 N
2. F_c = 8624 N
3. v_max = 30.04 m/s
4. v = 3.412 m/s
5. T = 22.25 N
6. v_max = 23.1 m/s

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