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 5 kg and length 2.4 m rotates about an axis O perpendicular to the rod, 1.1 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 5 kgL = 2.4 md = 1.1 m

I_O = kg·m²

2.Easy

A flywheel of mass 80 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1800 rpm. The driving torque is a constant 160 N·m and friction can be ignored. How long t does this take?

m = 80 kgk = 0.5 mn₁ = 0 rpmn₂ = 1800 rpmT = 160 N·m

t = s

3.Medium

A motor brings a flywheel with a moment of inertia of 8.5 kg·m² from rest up to 2500 rpm in 34 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 8.5 kg·m²n = 2500 rpmt = 34 s

P_avg = kW

4.Medium

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9.5 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 speed v of the block after it has fallen 2.5 m.

m = 7.5 kgM = 9.5 kgR = 0.4 mg = 9.81 m/s²h = 2.5 m

v = m/s

5.Hard

A thin hoop of mass 14.5 kg rolls without slipping at 6 m/s. What percentage p of its total kinetic energy is rotational?

m = 14.5 kgv = 6 m/sI = m·r²

p = %

6.Hard

A solid sphere of mass 9.5 kg rolls without slipping at 6 m/s. What percentage p of its total kinetic energy is rotational?

m = 9.5 kgv = 6 m/sI = (2/5)·m·r²

p = %

Answer key

1. I_O = 8.45 kg·m²
2. t = 23.56 s
3. P_avg = 8.567 kW
4. v = 5.48 m/s
5. p = 50 %
6. p = 28.57 %

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