1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?
v = 200 km/hamax = 2 m/s²
rmin = m
Circular motion worksheet with answers
2.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 120 km/h?
v = 120 km/hamax = 1.5 m/s²
rmin = m
3.Medium
A small ball on a string of length 1.3 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 1.3 mθ = 20°g = 9.81 m/s²
T = s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.
r = 1.9 mμs = 0.5g = 9.81 m/s²
n = rpm
5.Hard
A ball on a string 0.8 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 = 0.8 mg = 9.81 m/s²
vmin = m/s
6.Hard
A 0.5 kg ball on a light string 1.2 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 = 0.5 kgr = 1.2 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
Answer key
- 1. rmin = 1543 m
- 2. rmin = 740.7 m
- 3. T = 2.217 s
- 4. n = 30.69 rpm
- 5. vmin = 2.801 m/s
- 6. Ttop = 5.579 N
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