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 1.1 kg stone is whirled in a horizontal circle of radius 1.7 m on a smooth, level table, held by a string that breaks at a tension of 80 N. Find the highest speed v_max the stone can have.

m = 1.1 kgr = 1.7 mT_max = 80 N

v_max = m/s

2.Easy

A 600 kg car drives around a flat curve of radius 200 m at a constant 10 m/s. Find the inward (centripetal) force F_c needed.

m = 600 kgv = 10 m/sr = 200 m

F_c = N

3.Medium

A road engineer wants cars to take a curve of radius 270 m at 70 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 270 mv = 70 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 55 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 55 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 60 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 60 mθ = 15°μ_s = 0.1g = 9.81 m/s²

v_min = m/s

6.Hard

A 0.4 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 0.5 mv = 9 m/sg = 9.81 m/s²

T = N

Answer key

1. v_max = 11.12 m/s
2. F_c = 300 N
3. θ = 8.124 °
4. v_max = 16.42 m/s
5. v_min = 9.812 m/s
6. T = 68.72 N

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