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 200 m at a constant 30 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 30 m/sr = 200 m

F_c = N

2.Easy

An 800 kg car drives around a flat curve of radius 80 m at a constant 18 m/s. Find the inward (centripetal) force F_c needed.

m = 800 kgv = 18 m/sr = 80 m

F_c = N

3.Medium

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 135 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 90 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 90 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 210 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.3. 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 = 210 mθ = 25°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

6.Hard

A 1.9 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 1.1 mv = 5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 6300 N
2. F_c = 3240 N
3. v_max = 19.93 m/s
4. v_max = 18.79 m/s
5. v_max = 42.84 m/s
6. T = 61.82 N

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