1.Easy
A 1.6 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 60 N. Find the highest speed vmax the stone can have.
m = 1.6 kgr = 1.9 mTmax = 60 N
vmax = m/s
Circular motion worksheet with answers
2.Easy
A small object sits 115 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find the speed v of the object.
n = 120 rpmr = 1.15 m
v = m/s
3.Medium
A car takes a flat curve of radius 50 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 = 50 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.
r = 4 mμs = 0.8g = 9.81 m/s²
ω = rad/s
5.Hard
A 1.8 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 1.8 kgr = 0.9 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A curve of radius 150 m is banked at 12°, 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 = 150 mθ = 12°μs = 0.1g = 9.81 m/s²
vmax = m/s
Answer key
- 1. vmax = 8.441 m/s
- 2. v = 14.45 m/s
- 3. vmax = 18.53 m/s
- 4. ω = 1.751 rad/s
- 5. Ttop = 56.21 N
- 6. vmax = 21.68 m/s
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