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 1400 kg car drives around a flat curve of radius 80 m at a constant 8 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 8 m/sr = 80 m

a_c = m/s²

2.Easy

A small object sits 30 cm from the axis of a disc that turns at a steady 45 revolutions per minute. Find the speed v of the object.

n = 45 rpmr = 0.3 m

v = m/s

3.Medium

A road engineer wants cars to take a curve of radius 280 m at 40 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 280 mv = 40 km/hg = 9.81 m/s²

θ = °

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 50 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 50 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 0.7 kg ball on a string 1.1 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 = 0.7 kgr = 1.1 mv = 5.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.8 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 10.5 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 = 0.8 kgr = 1.1 mv_bottom = 10.5 m/sg = 9.81 m/s²

T_top = N

Answer key

1. a_c = 0.8 m/s²
2. v = 1.414 m/s
3. θ = 2.573 °
4. v_max = 22.15 m/s
5. T = 26.12 N
6. T_top = 40.94 N

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