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 160 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 27 m/sr = 160 m

F_c = N

2.Easy

A 1200 kg car drives around a flat curve of radius 150 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1200 kgv = 9 m/sr = 150 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 180 m at 50 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 180 mv = 50 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 80 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 80 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.5 kg cart is released from rest at a height of 20.5 m on a frictionless track and runs through a vertical loop of radius 5 m. Use g = 9.81 m/s². Find the normal force N_bottom of the track on the cart at the bottom of the loop.

m = 1.5 kgh = 20.5 mR = 5 mg = 9.81 m/s²

N_bottom = N

6.Hard

A ball on a string 1.3 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1.3 mg = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 6379 N
2. a_c = 0.54 m/s²
3. θ = 6.234 °
4. v_max = 21.7 m/s
5. N_bottom = 135.4 N
6. v_min = 3.571 m/s

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