Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A uniform slender rod of mass 11.5 kg and length 2.8 m rotates about an axis O perpendicular to the rod, 1.2 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 11.5 kgL = 2.8 md = 1.2 m

I_O = kg·m²

2.Easy

A flywheel of mass 90 kg with a radius of gyration of 0.2 m is accelerated uniformly from 200 rpm to 1400 rpm. The driving torque is a constant 230 N·m and friction can be ignored. How long t does this take?

m = 90 kgk = 0.2 mn₁ = 200 rpmn₂ = 1400 rpmT = 230 N·m

t = s

3.Medium

A motor delivers a torque of 320 N·m at 2000 rpm. Find its power output P in kW.

T = 320 N·mn = 2000 rpm

P = kW

4.Medium

A 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 13 kg and radius 0.1 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 = 12.5 kgM = 13 kgR = 0.1 mg = 9.81 m/s²

T = N

5.Hard

A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2 m down the slope?

θ = 40°I = (2/5)·m·r²g = 9.81 m/s²s = 2 m

t = s

6.Hard

A solid sphere of mass 2.5 kg rolls without slipping at 2.5 m/s. Find its total kinetic energy E_k.

m = 2.5 kgv = 2.5 m/sI = (2/5)·m·r²

E_k = J

Answer key

1. I_O = 24.07 kg·m²
2. t = 1.967 s
3. P = 67.02 kW
4. T = 41.95 N
5. t = 0.9424 s
6. E_k = 10.94 J

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