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 230 kg has a radius of gyration of 0.3 m about its axis. It spins at 1500 rpm. Find its kinetic energy E_k in kJ.

M = 230 kgk = 0.3 mn = 1500 rpm

E_k = kJ

2.Easy

A flywheel of mass 40 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1500 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.35 mn₁ = 0 rpmn₂ = 1500 rpmt = 15 s

T = N·m

3.Medium

A flywheel with a moment of inertia of 34.5 kg·m² spins at 700 rpm. A brake applies a constant friction torque of 40 N·m. How many revolutions N does the flywheel make before it stops?

I = 34.5 kg·m²n = 700 rpmT_b = 40 N·m

N = rev

4.Medium

A uniform slender rod of mass 2 kg and length 0.6 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 = 2 kgL = 0.6 mg = 9.81 m/s²

α = rad/s²

5.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 1.5 m along the slope.

θ = 20°s = 1.5 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A thin hoop of mass 12.5 kg rolls without slipping at 2 m/s. Find its total kinetic energy E_k.

m = 12.5 kgv = 2 m/sI = m·r²

E_k = J

Answer key

1. E_k = 255.4 kJ
2. T = 51.31 N·m
3. N = 368.8 rev
4. α = 24.53 rad/s²
5. v = 2.458 m/s
6. E_k = 50 J

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