1.Easy
A 1.7 kg stone is whirled in a horizontal circle of radius 1 m on a smooth, level table, held by a string that breaks at a tension of 150 N. Find the highest speed vmax the stone can have.
m = 1.7 kgr = 1 mTmax = 150 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A 0.3 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 190 N. Find the highest speed vmax the stone can have.
m = 0.3 kgr = 1.1 mTmax = 190 N
vmax = m/s
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.7 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 = 2.7 mμs = 0.3g = 9.81 m/s²
ω = rad/s
4.Medium
A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 25° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.
L = 0.9 mθ = 25°g = 9.81 m/s²
v = m/s
5.Hard
A 1.8 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.8 kgr = 1.2 mv = 8 m/sg = 9.81 m/s²
T = N
6.Hard
A 5 kg cart is released from rest at a height of 2.3 m on a frictionless track and runs through a vertical loop of radius 0.5 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 = 5 kgh = 2.3 mR = 0.5 mg = 9.81 m/s²
Nbottom = N
Answer key
- 1. vmax = 9.393 m/s
- 2. vmax = 26.39 m/s
- 3. ω = 3.48 rad/s
- 4. v = 1.319 m/s
- 5. T = 113.7 N
- 6. Nbottom = 500.3 N
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