1.Easy
A 0.4 kg stone is whirled in a horizontal circle of radius 0.9 m on a smooth, level table, held by a string that breaks at a tension of 170 N. Find the highest speed vmax the stone can have.
m = 0.4 kgr = 0.9 mTmax = 170 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A small object sits 105 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration ac.
n = 30 rpmr = 1.05 m
ac = m/s²
3.Medium
A car drives over the top of a hump in the road, which is a circular arc of radius 40 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?
r = 40 mg = 9.81 m/s²
vmax = m/s
4.Medium
A car takes a flat curve of radius 40 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 40 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
A 1.5 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.5 kgr = 1.2 mv = 3.5 m/sg = 9.81 m/s²
T = N
6.Hard
A 1.1 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 1.1 kgr = 1 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. vmax = 19.56 m/s
- 2. ac = 10.36 m/s²
- 3. vmax = 19.81 m/s
- 4. vmax = 15.34 m/s
- 5. T = 30.03 N
- 6. Ttop = 56.05 N
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