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 6 kg and length 1.4 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 6 kgL = 1.4 md = 0.2 m

I_O = kg·m²

2.Easy

A flywheel is a uniform solid disc of mass 160 kg and radius 0.5 m. It spins at 2400 rpm. Find its kinetic energy E_k in kJ.

M = 160 kgR = 0.5 mn = 2400 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 14.5 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 15 N·m. How many revolutions N does the flywheel make before it stops?

I = 14.5 kg·m²n = 1800 rpmT_b = 15 N·m

N = rev

4.Medium

A uniform slender rod of mass 12.5 kg and length 1.9 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 = 12.5 kgL = 1.9 mg = 9.81 m/s²

α = rad/s²

5.Hard

A thin hoop rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 35°I = m·r²g = 9.81 m/s²

a = m/s²

6.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7.5 m along the slope.

θ = 35°s = 7.5 mI = ½·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. I_O = 1.22 kg·m²
2. E_k = 631.7 kJ
3. N = 2733 rev
4. α = 7.745 rad/s²
5. a = 2.813 m/s²
6. v = 7.501 m/s

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