1.Easy
For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?
v = 160 km/hamax = 0.5 m/s²
rmin = m
Circular motion worksheet with answers
2.Easy
A 1100 kg car drives around a flat curve of radius 30 m at a constant 15 m/s. Find its centripetal acceleration ac.
m = 1100 kgv = 15 m/sr = 30 m
ac = m/s²
3.Medium
In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.6 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 angular speed ω in rad/s.
r = 3.6 mμs = 0.6g = 9.81 m/s²
ω = rad/s
4.Medium
An 800 kg car drives over the top of a hump in the road at 29 m/s. The top of the hump is a circular arc of radius 110 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.
m = 800 kgv = 29 m/sr = 110 mg = 9.81 m/s²
N = N
5.Hard
A 0.8 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 12 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.
m = 0.8 kgr = 1.3 mvbottom = 12 m/sg = 9.81 m/s²
Ttop = N
6.Hard
A 1.8 kg ball on a string 1.5 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 = 1.8 kgr = 1.5 mv = 7 m/sg = 9.81 m/s²
T = N
Answer key
- 1. rmin = 3951 m
- 2. ac = 7.5 m/s²
- 3. ω = 2.131 rad/s
- 4. N = 1732 N
- 5. Ttop = 49.38 N
- 6. T = 76.46 N
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