1.Easy
A uniform slender rod of mass 8 kg and length 1.9 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 8 kgL = 1.9 md = 0.85 m
IO = kg·m²
Rigid-body rotation worksheet with answers
2.Easy
A flywheel of mass 270 kg has a radius of gyration of 0.4 m about its axis. It spins at 900 rpm. Find its kinetic energy Ek in kJ.
M = 270 kgk = 0.4 mn = 900 rpm
Ek = kJ
3.Medium
A uniform slender rod of mass 9.5 kg and length 1 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
m = 9.5 kgL = 1 mg = 9.81 m/s²
atip = m/s²
4.Medium
An 11 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9.5 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
m = 11 kgM = 9.5 kgR = 0.4 mg = 9.81 m/s²
a = m/s²
5.Hard
A uniform slender rod of mass 8 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 320 m/s hits the rod 0.87 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
M = 8 kgL = 1.3 mm = 30 gv = 320 m/sd = 0.87 m
ω = rad/s
6.Hard
A solid cylinder rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
θ = 25°I = ½·m·r²g = 9.81 m/s²
μs =
Answer key
- 1. IO = 8.187 kg·m²
- 2. Ek = 191.9 kJ
- 3. atip = 14.71 m/s²
- 4. a = 6.851 m/s²
- 5. ω = 1.844 rad/s
- 6. μs = 0.1554
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