1.Easy
A uniform slender rod of mass 9.5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 0.65 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 9.5 kgL = 2.7 md = 0.65 m
IO = kg·m²
Rigid-body rotation worksheet with answers
2.Easy
A flywheel of mass 40 kg has a radius of gyration of 0.2 m about its axis. It spins at 400 rpm. Find its kinetic energy Ek in kJ.
M = 40 kgk = 0.2 mn = 400 rpm
Ek = kJ
3.Medium
A uniform slender rod of mass 8 kg and length 2.4 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 = 8 kgL = 2.4 mg = 9.81 m/s²
α = rad/s²
4.Medium
A motor brings a flywheel with a moment of inertia of 25.5 kg·m² from rest up to 2300 rpm in 42 s. Ignoring losses, find the average power Pavg it delivers, in kW.
I = 25.5 kg·m²n = 2300 rpmt = 42 s
Pavg = kW
5.Hard
A solid sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 6.5 m along the slope.
θ = 35°s = 6.5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
I0 = 2 kg·m²m = 2 × 4 kgr1 = 0.6 mr2 = 0.2 mn1 = 25 rpm
n2 = rpm
Answer key
- 1. IO = 9.785 kg·m²
- 2. Ek = 1.404 kJ
- 3. α = 6.131 rad/s²
- 4. Pavg = 17.61 kW
- 5. v = 7.228 m/s
- 6. n2 = 52.59 rpm
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