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 1100 kg car drives around a flat curve of radius 110 m at a constant 10 m/s. Find the inward (centripetal) force F_c needed.

m = 1100 kgv = 10 m/sr = 110 m

F_c = N

2.Easy

A 600 kg car drives around a flat curve of radius 80 m at a constant 12 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 12 m/sr = 80 m

F_c = N

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 70 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 70 mg = 9.81 m/s²

v_max = m/s

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.1 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.1 mμ_s = 0.8g = 9.81 m/s²

ω = rad/s

5.Hard

A 1.9 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 1.5 mv = 4.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.6 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 10 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 = 1.6 kgr = 1 mv_bottom = 10 m/sg = 9.81 m/s²

T_top = N

Answer key

1. F_c = 1000 N
2. F_c = 1080 N
3. v_max = 26.2 m/s
4. ω = 2.416 rad/s
5. T = 44.29 N
6. T_top = 81.52 N

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