1.Easy
A small object sits 75 cm from the axis of a disc that turns at a steady 45 revolutions per minute. Find its centripetal acceleration ac.
n = 45 rpmr = 0.75 m
ac = m/s²
Circular motion worksheet with answers
2.Easy
A small object sits 110 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration ac.
n = 200 rpmr = 1.1 m
ac = m/s²
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.
r = 3.9 mμs = 0.7g = 9.81 m/s²
n = rpm
4.Medium
A small ball on a string of length 0.5 m moves in a horizontal circle so that the string makes a constant angle of 35° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 0.5 mθ = 35°g = 9.81 m/s²
T = s
5.Hard
A 0.5 kg cart is released from rest at a height of 2.1 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 = 0.5 kgh = 2.1 mR = 0.5 mg = 9.81 m/s²
Nbottom = N
6.Hard
A 1.6 kg ball on a string 0.5 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 = 1.6 kgr = 0.5 mv = 9 m/sg = 9.81 m/s²
T = N
Answer key
- 1. ac = 16.65 m/s²
- 2. ac = 482.5 m/s²
- 3. n = 18.1 rpm
- 4. T = 1.284 s
- 5. Nbottom = 46.11 N
- 6. T = 274.9 N
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