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 1300 kg car drives around a flat curve of radius 50 m at a constant 26 m/s. Find the inward (centripetal) force F_c needed.

m = 1300 kgv = 26 m/sr = 50 m

F_c = N

2.Easy

A 1500 kg car drives around a flat curve of radius 140 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 1500 kgv = 17 m/sr = 140 m

F_c = N

3.Medium

A 900 kg car drives over the top of a hump in the road at 19 m/s. The top of the hump is a circular arc of radius 75 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 900 kgv = 19 m/sr = 75 mg = 9.81 m/s²

N = N

4.Medium

A small ball on a string of length 0.9 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 speed v of the ball.

L = 0.9 mθ = 45°g = 9.81 m/s²

v = m/s

5.Hard

A ball on a string 1.3 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1.3 mg = 9.81 m/s²

v_min = m/s

6.Hard

A curve of radius 140 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.3. 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 = 140 mθ = 30°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 17576 N
2. F_c = 3096 N
3. N = 4497 N
4. v = 2.499 m/s
5. v_min = 3.571 m/s
6. v_max = 38.18 m/s

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