1.Easy
A uniform slender rod of mass 6.5 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 6.5 kgL = 3 md = 0.55 m
IO = kg·m²
Rigid-body rotation worksheet with answers
2.Easy
A flywheel is a uniform solid disc of mass 190 kg and radius 0.3 m. It spins at 3000 rpm. Find its kinetic energy Ek in kJ.
M = 190 kgR = 0.3 mn = 3000 rpm
Ek = kJ
3.Medium
A uniform slender rod of mass 3 kg and length 1.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
m = 3 kgL = 1.2 mmball = 1 kgg = 9.81 m/s²
v = m/s
4.Medium
A uniform slender rod of mass 14 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 its angular acceleration α just after release.
m = 14 kgL = 1 mg = 9.81 m/s²
α = rad/s²
5.Hard
A hollow sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
θ = 40°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²
6.Hard
A uniform slender rod of mass 4.5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 500 m/s hits the rod 0.3 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
M = 4.5 kgL = 0.5 mm = 20 gv = 500 m/sd = 0.3 m
ω = rad/s
Answer key
- 1. IO = 6.841 kg·m²
- 2. Ek = 421.9 kJ
- 3. v = 5.425 m/s
- 4. α = 14.71 rad/s²
- 5. a = 3.783 m/s²
- 6. ω = 7.962 rad/s
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