1.Easy
A uniform slender rod of mass 11 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.3 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 11 kgL = 2.7 md = 1.3 m
IO = kg·m²
Rigid-body rotation worksheet with answers
2.Easy
A flywheel of mass 150 kg has a radius of gyration of 0.45 m about its axis. It spins at 700 rpm. Find its kinetic energy Ek in kJ.
M = 150 kgk = 0.45 mn = 700 rpm
Ek = kJ
3.Medium
A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 11.5 kg and radius 0.3 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 3.5 m.
m = 7.5 kgM = 11.5 kgR = 0.3 mg = 9.81 m/s²h = 3.5 m
v = m/s
4.Medium
A 13 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 16 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.
m = 13 kgM = 16 kgR = 0.2 mg = 9.81 m/s²
T = N
5.Hard
A solid sphere starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.1 m. Find its angular velocity ω after it has rolled 5 m along the slope.
θ = 40°s = 5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.1 m
ω = rad/s
6.Hard
A thin hoop of mass 14 kg rolls without slipping at 7 m/s. Find its total kinetic energy Ek.
m = 14 kgv = 7 m/sI = m·r²
Ek = J
Answer key
- 1. IO = 25.27 kg·m²
- 2. Ek = 81.61 kJ
- 3. v = 6.235 m/s
- 4. T = 48.58 N
- 5. ω = 67.11 rad/s
- 6. Ek = 686 J
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