1.Easy
A 0.6 kg stone is whirled in a horizontal circle of radius 1.2 m on a smooth, level table, held by a string that breaks at a tension of 80 N. Find the highest speed vmax the stone can have.
m = 0.6 kgr = 1.2 mTmax = 80 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 1400 kg car drives around a flat curve of radius 20 m at a constant 22 m/s. Find its centripetal acceleration ac.
m = 1400 kgv = 22 m/sr = 20 m
ac = m/s²
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.8 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 2.8 mμs = 0.5g = 9.81 m/s²
ω = rad/s
4.Medium
A car takes a flat curve of radius 60 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 60 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
A 2.5 kg cart is released from rest at a height of 35 m on a frictionless track and runs through a vertical loop of radius 7 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 = 2.5 kgh = 35 mR = 7 mg = 9.81 m/s²
Nbottom = N
6.Hard
A curve of radius 110 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.
r = 110 mθ = 10°μs = 0.1g = 9.81 m/s²
vmax = m/s
Answer key
- 1. vmax = 12.65 m/s
- 2. ac = 24.2 m/s²
- 3. ω = 2.647 rad/s
- 4. vmax = 20.3 m/s
- 5. Nbottom = 269.8 N
- 6. vmax = 17.42 m/s
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