1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?
v = 160 km/hamax = 1.5 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A small object sits 100 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find the speed v of the object.
n = 90 rpmr = 1 m
v = m/s
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.5 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 rotation rate n in revolutions per minute.
r = 3.5 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.2 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 = 3.2 mμs = 0.8g = 9.81 m/s²
ω = rad/s
5.Hard
A curve of radius 240 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.
r = 240 mθ = 10°μs = 0.15g = 9.81 m/s²
vmin = m/s
6.Hard
A ball on a string 1.4 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?
r = 1.4 mg = 9.81 m/s²
vmin = m/s
Answer key
- 1. rmin = 1317 m
- 2. v = 9.425 m/s
- 3. n = 29.19 rpm
- 4. ω = 1.958 rad/s
- 5. vmin = 7.771 m/s
- 6. vmin = 3.706 m/s
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