1.Easy
A flywheel of mass 10 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1800 rpm. This takes 4 s. Ignoring friction, find the constant torque T needed.
m = 10 kgk = 0.1 mn1 = 0 rpmn2 = 1800 rpmt = 4 s
T = N·m
Rigid-body rotation worksheet with answers
2.Easy
A flywheel of mass 110 kg has a radius of gyration of 0.4 m about its axis. It spins at 300 rpm. Find its kinetic energy Ek in kJ.
M = 110 kgk = 0.4 mn = 300 rpm
Ek = kJ
3.Medium
A 14.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 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 = 14.5 kgM = 8 kgR = 0.2 mg = 9.81 m/s²
T = N
4.Medium
A uniform slender rod of mass 4 kg and length 1.5 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 speed v of the free end as the rod swings through the vertical position.
m = 4 kgL = 1.5 mg = 9.81 m/s²
v = m/s
5.Hard
A solid sphere of mass 17 kg rolls without slipping at 4 m/s. Find its total kinetic energy Ek.
m = 17 kgv = 4 m/sI = (2/5)·m·r²
Ek = J
6.Hard
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 10 m along the slope.
θ = 10°s = 10 mI = ½·m·r²g = 9.81 m/s²r = 0.15 m
ω = rad/s
Answer key
- 1. T = 4.712 N·m
- 2. Ek = 8.685 kJ
- 3. T = 30.76 N
- 4. v = 6.644 m/s
- 5. Ek = 190.4 J
- 6. ω = 31.77 rad/s
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