1.Easy
A 2 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 70 N. Find the highest speed vmax the stone can have.
m = 2 kgr = 1.4 mTmax = 70 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 1.5 kg stone is whirled in a horizontal circle of radius 1.8 m on a smooth, level table, held by a string that breaks at a tension of 30 N. Find the highest speed vmax the stone can have.
m = 1.5 kgr = 1.8 mTmax = 30 N
vmax = m/s
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 2.3 mμs = 0.4g = 9.81 m/s²
ω = rad/s
4.Medium
A car takes a flat curve of radius 55 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 = 55 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.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 vmin at the top for which the string just stays tight?
r = 0.5 mg = 9.81 m/s²
vmin = m/s
6.Hard
A 1.5 kg cart is released from rest at a height of 31.35 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 Nbottom of the track on the cart at the bottom of the loop.
m = 1.5 kgh = 31.35 mR = 9.5 mg = 9.81 m/s²
Nbottom = N
Answer key
- 1. vmax = 7 m/s
- 2. vmax = 6 m/s
- 3. ω = 3.265 rad/s
- 4. vmax = 17.99 m/s
- 5. vmin = 2.215 m/s
- 6. Nbottom = 111.8 N
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