1.Easy
A flywheel is a uniform solid disc of mass 20 kg and radius 0.45 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.
M = 20 kgR = 0.45 mn = 1000 rpm
Ek = kJ
Rigid-body rotation worksheet with answers
2.Easy
A flywheel is a uniform solid disc of mass 300 kg and radius 0.5 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.
M = 300 kgR = 0.5 mn = 1000 rpm
Ek = kJ
3.Medium
A uniform slender rod of mass 12 kg and length 1.5 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 = 12 kgL = 1.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
A uniform slender rod of mass 2.5 kg and length 0.7 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 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 = 2.5 kgL = 0.7 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
5.Hard
A solid sphere of mass 6 kg rolls without slipping at 4.5 m/s. What percentage p of its total kinetic energy is rotational?
m = 6 kgv = 4.5 m/sI = (2/5)·m·r²
p = %
6.Hard
A person stands on a frictionless turntable and holds a 4.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 2.5 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 = 2.5 kg·m²m = 2 × 4.5 kgr1 = 0.85 mr2 = 0.2 mn1 = 25 rpm
n2 = rpm
Answer key
- 1. Ek = 11.1 kJ
- 2. Ek = 205.6 kJ
- 3. α = 9.81 rad/s²
- 4. v = 3.931 m/s
- 5. p = 28.57 %
- 6. n2 = 78.69 rpm
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