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 700 kg car drives around a flat curve of radius 120 m at a constant 29 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 29 m/sr = 120 m

a_c = m/s²

2.Easy

An 800 kg car drives around a flat curve of radius 180 m at a constant 28 m/s. Find its centripetal acceleration a_c.

m = 800 kgv = 28 m/sr = 180 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 115 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 = 115 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A curve of radius 200 m is banked at 10°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 200 mθ = 10°g = 9.81 m/s²

v = m/s

5.Hard

A 4 kg cart is released from rest at a height of 20.15 m on a frictionless track and runs through a vertical loop of radius 6.5 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 = 4 kgh = 20.15 mR = 6.5 mg = 9.81 m/s²

N_bottom = N

6.Hard

A 1.2 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 1 mv = 6 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 7.008 m/s²
2. a_c = 4.356 m/s²
3. v_max = 18.4 m/s
4. v = 18.6 m/s
5. N_bottom = 282.5 N
6. T = 54.97 N

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