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 900 kg car drives around a flat curve of radius 150 m at a constant 27 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 27 m/sr = 150 m

a_c = m/s²

2.Easy

A 1800 kg car drives around a flat curve of radius 80 m at a constant 10 m/s. Find the inward (centripetal) force F_c needed.

m = 1800 kgv = 10 m/sr = 80 m

F_c = N

3.Medium

A road engineer wants cars to take a curve of radius 150 m at 80 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 150 mv = 80 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 85 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 = 85 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 250 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.3. 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 = 250 mθ = 30°μ_s = 0.3g = 9.81 m/s²

v_min = m/s

6.Hard

A 2.5 kg cart is released from rest at a height of 45.6 m on a frictionless track and runs through a vertical loop of radius 9.5 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 = 2.5 kgh = 45.6 mR = 9.5 mg = 9.81 m/s²

N_bottom = N

Answer key

1. a_c = 4.86 m/s²
2. F_c = 2250 N
3. θ = 18.55 °
4. v_max = 20.42 m/s
5. v_min = 24.08 m/s
6. N_bottom = 260 N

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