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 1800 kg car drives around a flat curve of radius 150 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 9 m/sr = 150 m

a_c = m/s²

2.Easy

A 0.7 kg stone is whirled in a horizontal circle of radius 1.6 m on a smooth, level table, held by a string that breaks at a tension of 120 N. Find the highest speed v_max the stone can have.

m = 0.7 kgr = 1.6 mT_max = 120 N

v_max = m/s

3.Medium

A car takes a flat curve of radius 105 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 = 105 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 110 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 = 110 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.2 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 = 1.2 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.7 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 1.3 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 0.54 m/s²
2. v_max = 16.56 m/s
3. v_max = 20.3 m/s
4. v_max = 29.38 m/s
5. v_min = 3.431 m/s
6. T = 90.23 N

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