1.Easy
A 1.2 kg stone is whirled in a horizontal circle of radius 1.1 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed vmax the stone can have.
m = 1.2 kgr = 1.1 mTmax = 200 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 1.7 kg stone is whirled in a horizontal circle of radius 1.7 m on a smooth, level table, held by a string that breaks at a tension of 110 N. Find the highest speed vmax the stone can have.
m = 1.7 kgr = 1.7 mTmax = 110 N
vmax = m/s
3.Medium
A small ball on a string of length 1.9 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.
L = 1.9 mθ = 30°g = 9.81 m/s²
v = m/s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 2 mμs = 0.3g = 9.81 m/s²
ω = rad/s
5.Hard
A 1 kg cart is released from rest at a height of 8 m on a frictionless track and runs through a vertical loop of radius 2.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.
m = 1 kgh = 8 mR = 2.5 mg = 9.81 m/s²
Ntop = N
6.Hard
A 0.4 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 0.4 kgr = 0.7 mv = 9 m/sg = 9.81 m/s²
T = N
Answer key
- 1. vmax = 13.54 m/s
- 2. vmax = 10.49 m/s
- 3. v = 2.32 m/s
- 4. ω = 4.044 rad/s
- 5. Ntop = 13.73 N
- 6. T = 50.21 N
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