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 small object sits 145 cm from the axis of a disc that turns at a steady 60 revolutions per minute. Find the speed v of the object.

n = 60 rpmr = 1.45 m

v = m/s

2.Easy

A small object sits 90 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 = 0.9 m

v = m/s

3.Medium

A car takes a flat curve of radius 25 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 25 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 360 m at 50 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 360 mv = 50 km/hg = 9.81 m/s²

θ = °

5.Hard

A 1.8 kg ball on a light string 1.1 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 = 1.8 kgr = 1.1 mv_bottom = 8.5 m/sg = 9.81 m/s²

T_top = N

6.Hard

A curve of radius 260 m is banked at 10°, 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 = 260 mθ = 10°μ_s = 0.2g = 9.81 m/s²

v_max = m/s

Answer key

1. v = 9.111 m/s
2. v = 4.241 m/s
3. v_max = 13.1 m/s
4. θ = 3.126 °
5. T_top = 29.94 N
6. v_max = 31.54 m/s

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