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 flywheel of mass 20 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 1500 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 20 kgk = 0.6 mn₁ = 0 rpmn₂ = 1500 rpmt = 15 s

T = N·m

2.Easy

A flywheel of mass 250 kg has a radius of gyration of 0.5 m about its axis. It spins at 1000 rpm. Find its kinetic energy E_k in kJ.

M = 250 kgk = 0.5 mn = 1000 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 17.5 kg and length 2.6 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 = 17.5 kgL = 2.6 mg = 9.81 m/s²

α = rad/s²

4.Medium

A motor brings a flywheel with a moment of inertia of 22 kg·m² from rest up to 3000 rpm in 45 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 22 kg·m²n = 3000 rpmt = 45 s

P_avg = kW

5.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 1 m along the slope.

θ = 15°s = 1 mI = ½·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A solid sphere of mass 14 kg rolls without slipping at 9 m/s. Find its total kinetic energy E_k.

m = 14 kgv = 9 m/sI = (2/5)·m·r²

E_k = J

Answer key

1. T = 75.4 N·m
2. E_k = 342.7 kJ
3. α = 5.66 rad/s²
4. P_avg = 24.13 kW
5. v = 1.84 m/s
6. E_k = 793.8 J

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