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 60 kg has a radius of gyration of 0.15 m about its axis. It spins at 1100 rpm. Find its kinetic energy E_k in kJ.

M = 60 kgk = 0.15 mn = 1100 rpm

E_k = kJ

2.Easy

A flywheel of mass 170 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 1200 rpm. The driving torque is a constant 300 N·m and friction can be ignored. How long t does this take?

m = 170 kgk = 0.6 mn₁ = 0 rpmn₂ = 1200 rpmT = 300 N·m

t = s

3.Medium

A motor brings a flywheel with a moment of inertia of 30.5 kg·m² from rest up to 1100 rpm in 51 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 30.5 kg·m²n = 1100 rpmt = 51 s

P_avg = kW

4.Medium

A flywheel with a moment of inertia of 21.5 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 55 N·m. How many revolutions N does the flywheel make before it stops?

I = 21.5 kg·m²n = 2200 rpmT_b = 55 N·m

N = rev

5.Hard

A solid sphere of mass 8.5 kg rolls without slipping at 10 m/s. What percentage p of its total kinetic energy is rotational?

m = 8.5 kgv = 10 m/sI = (2/5)·m·r²

p = %

6.Hard

A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 5 m down the slope?

θ = 20°I = ½·m·r²g = 9.81 m/s²s = 5 m

t = s

Answer key

1. E_k = 8.957 kJ
2. t = 25.64 s
3. P_avg = 3.968 kW
4. N = 1651 rev
5. p = 28.57 %
6. t = 2.114 s

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