1.Easy
A uniform slender rod of mass 3 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.15 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 3 kgL = 2.7 md = 1.15 m
IO = kg·m²
Rigid-body rotation worksheet with answers
2.Easy
A flywheel of mass 10 kg with a radius of gyration of 0.3 m is accelerated uniformly from 200 rpm to 2200 rpm. The driving torque is a constant 6.7 N·m and friction can be ignored. How long t does this take?
m = 10 kgk = 0.3 mn1 = 200 rpmn2 = 2200 rpmT = 6.7 N·m
t = s
3.Medium
A uniform slender rod of mass 12 kg and length 1.6 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 = 12 kgL = 1.6 mg = 9.81 m/s²
atip = m/s²
4.Medium
A uniform slender rod of mass 7.5 kg and length 1.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 0.5 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 = 7.5 kgL = 1.2 mmball = 0.5 kgg = 9.81 m/s²
v = m/s
5.Hard
A thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 10 m along the slope.
θ = 25°s = 10 mI = m·r²g = 9.81 m/s²
v = m/s
6.Hard
A hollow sphere of mass 10 kg rolls without slipping at 9.5 m/s. What percentage p of its total kinetic energy is rotational?
m = 10 kgv = 9.5 m/sI = (2/3)·m·r²
p = %
Answer key
- 1. IO = 5.79 kg·m²
- 2. t = 28.13 s
- 3. atip = 14.71 m/s²
- 4. v = 5.775 m/s
- 5. v = 6.439 m/s
- 6. p = 40 %
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