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 1200 kg car drives around a flat curve of radius 80 m at a constant 12 m/s. Find its centripetal acceleration a_c.

m = 1200 kgv = 12 m/sr = 80 m

a_c = m/s²

2.Easy

A 0.1 kg stone is whirled in a horizontal circle of radius 1.3 m on a smooth, level table, held by a string that breaks at a tension of 130 N. Find the highest speed v_max the stone can have.

m = 0.1 kgr = 1.3 mT_max = 130 N

v_max = m/s

3.Medium

A car takes a flat curve of radius 150 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 150 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 290 m at 40 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 290 mv = 40 km/hg = 9.81 m/s²

θ = °

5.Hard

A 0.2 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 0.7 mv = 7 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 0.5 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 = 0.5 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 1.8 m/s²
2. v_max = 41.11 m/s
3. v_max = 34.31 m/s
4. θ = 2.485 °
5. T = 15.96 N
6. v_min = 2.215 m/s

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