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 8.5 kg and length 2.5 m rotates about an axis O perpendicular to the rod, 0.65 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 8.5 kgL = 2.5 md = 0.65 m

I_O = kg·m²

2.Easy

A flywheel of mass 70 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 400 rpm. The driving torque is a constant 24 N·m and friction can be ignored. How long t does this take?

m = 70 kgk = 0.5 mn₁ = 0 rpmn₂ = 400 rpmT = 24 N·m

t = s

3.Medium

A flywheel with a moment of inertia of 3.5 kg·m² spins at 2600 rpm. A brake applies a constant friction torque of 135 N·m. How many revolutions N does the flywheel make before it stops?

I = 3.5 kg·m²n = 2600 rpmT_b = 135 N·m

N = rev

4.Medium

A flywheel with a moment of inertia of 3 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 40 N·m. How many revolutions N does the flywheel make before it stops?

I = 3 kg·m²n = 2100 rpmT_b = 40 N·m

N = rev

5.Hard

A solid sphere of mass 12 kg rolls without slipping at 3.5 m/s. Find its total kinetic energy E_k.

m = 12 kgv = 3.5 m/sI = (2/5)·m·r²

E_k = J

6.Hard

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 4 m along the slope.

θ = 40°s = 4 mI = m·r²g = 9.81 m/s²

v = m/s

Answer key

1. I_O = 8.018 kg·m²
2. t = 30.54 s
3. N = 152.9 rev
4. N = 288.6 rev
5. E_k = 102.9 J
6. v = 5.022 m/s

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