1.Easy
A flywheel of mass 110 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 900 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.
m = 110 kgk = 0.35 mn1 = 0 rpmn2 = 900 rpmt = 30 s
T = N·m
Rigid-body rotation worksheet with answers
2.Easy
A uniform slender rod of mass 3.5 kg and length 0.9 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.
m = 3.5 kgL = 0.9 md = 0.4 m
IO = kg·m²
3.Medium
A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 20 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
m = 6 kgM = 20 kgR = 0.4 mg = 9.81 m/s²
a = m/s²
4.Medium
A uniform slender rod of mass 1 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.
m = 1 kgL = 0.6 mg = 9.81 m/s²
ω = rad/s
5.Hard
A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2.5 m down the slope?
θ = 30°I = (2/5)·m·r²g = 9.81 m/s²s = 2.5 m
t = s
6.Hard
A thin hoop starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 9.5 m along the slope.
θ = 15°s = 9.5 mI = m·r²g = 9.81 m/s²r = 0.15 m
ω = rad/s
Answer key
- 1. T = 42.33 N·m
- 2. IO = 0.7963 kg·m²
- 3. a = 3.679 m/s²
- 4. ω = 7.004 rad/s
- 5. t = 1.195 s
- 6. ω = 32.74 rad/s
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