1.Easy
A 0.7 kg stone is whirled in a horizontal circle of radius 1.3 m on a smooth, level table, held by a string that breaks at a tension of 150 N. Find the highest speed vmax the stone can have.
m = 0.7 kgr = 1.3 mTmax = 150 N
vmax = m/s
Circular motion worksheet with answers
2.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 250 km/h?
v = 250 km/hamax = 2 m/s²
rmin = m
3.Medium
A small ball on a string of length 0.8 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.
L = 0.8 mθ = 50°g = 9.81 m/s²
T = s
4.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.1 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 = 2.1 mμs = 0.6g = 9.81 m/s²
n = rpm
5.Hard
A 1.3 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.3 kgr = 1.2 mv = 7 m/sg = 9.81 m/s²
T = N
6.Hard
A 1.3 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.
m = 1.3 kgr = 0.9 mv = 8.5 m/sg = 9.81 m/s²
T = N
Answer key
- 1. vmax = 16.69 m/s
- 2. rmin = 2411 m
- 3. T = 1.439 s
- 4. n = 26.65 rpm
- 5. T = 65.84 N
- 6. T = 117.1 N
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