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 1000 kg car drives around a flat curve of radius 70 m at a constant 29 m/s. Find the inward (centripetal) force F_c needed.

m = 1000 kgv = 29 m/sr = 70 m

F_c = N

2.Easy

A small object sits 145 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find the speed v of the object.

n = 300 rpmr = 1.45 m

v = m/s

3.Medium

A curve of radius 170 m is banked at 15°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 170 mθ = 15°g = 9.81 m/s²

v = m/s

4.Medium

A small ball on a string of length 1.8 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 time T for one revolution.

L = 1.8 mθ = 50°g = 9.81 m/s²

T = s

5.Hard

A 0.2 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.2 kgr = 0.9 mv_bottom = 8.5 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 5 kg cart is released from rest at a height of 33 m on a frictionless track and runs through a vertical loop of radius 10 m. Use g = 9.81 m/s². Find the normal force N_top of the track on the cart at the top of the loop.

m = 5 kgh = 33 mR = 10 mg = 9.81 m/s²

N_top = N

Answer key

1. F_c = 12014 N
2. v = 45.55 m/s
3. v = 21.14 m/s
4. T = 2.158 s
5. T_top = 6.246 N
6. N_top = 78.48 N

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