1.Easy
A flywheel of mass 80 kg with a radius of gyration of 0.3 m is accelerated uniformly from 700 rpm to 1900 rpm. This takes 27 s. Ignoring friction, find the constant torque T needed.
m = 80 kgk = 0.3 mn1 = 700 rpmn2 = 1900 rpmt = 27 s
T = N·m
Rigid-body rotation worksheet with answers
2.Easy
A pendulum is made of a uniform slender rod (1 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
mrod = 1 kgL = 0.5 mmsphere = 9 kgr = 0.1 md = 0.6 m
IO = kg·m²
3.Medium
A uniform slender rod of mass 6.5 kg and length 0.7 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 = 6.5 kgL = 0.7 mg = 9.81 m/s²
α = rad/s²
4.Medium
A 10 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.
m = 10 kgM = 6.5 kgR = 0.5 mg = 9.81 m/s²
α = rad/s²
5.Hard
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8.5 m along the slope.
θ = 40°s = 8.5 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
θ = 25°I = m·r²g = 9.81 m/s²
μs =
Answer key
- 1. T = 33.51 N·m
- 2. IO = 3.359 kg·m²
- 3. α = 21.02 rad/s²
- 4. α = 14.81 rad/s²
- 5. v = 8.454 m/s
- 6. μs = 0.2332
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