1.Easy
A small object sits 65 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.
n = 33 rpmr = 0.65 m
v = m/s
Circular motion worksheet with answers
2.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?
v = 250 km/hamax = 0.8 m/s²
rmin = m
3.Medium
A car takes a flat curve of radius 140 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.
r = 140 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.
r = 3.7 mμs = 0.6g = 9.81 m/s²
n = rpm
5.Hard
A curve of radius 120 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.25. 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 = 120 mθ = 15°μs = 0.25g = 9.81 m/s²
vmax = m/s
6.Hard
A 0.9 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 7 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 0.9 kgr = 0.5 mvbottom = 7 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. v = 2.246 m/s
- 2. rmin = 6028 m
- 3. vmax = 26.2 m/s
- 4. n = 20.07 rpm
- 5. vmax = 25.56 m/s
- 6. Ttop = 44.05 N
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