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 12 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 12 kgL = 2.7 md = 0.55 m

I_O = kg·m²

2.Easy

A flywheel is a uniform solid disc of mass 290 kg and radius 0.6 m. It spins at 1400 rpm. Find its kinetic energy E_k in kJ.

M = 290 kgR = 0.6 mn = 1400 rpm

E_k = kJ

3.Medium

A motor delivers a torque of 630 N·m at 3000 rpm. Find its power output P in kW.

T = 630 N·mn = 3000 rpm

P = kW

4.Medium

A uniform slender rod of mass 6 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 6 kgL = 1.6 mg = 9.81 m/s²

ω = rad/s

5.Hard

A uniform slender rod of mass 2 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 300 m/s hits the rod 0.28 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 2 kgL = 0.7 mm = 30 gv = 300 m/sd = 0.28 m

ω = rad/s

6.Hard

A solid sphere of mass 11 kg rolls without slipping at 2 m/s. What percentage p of its total kinetic energy is rotational?

m = 11 kgv = 2 m/sI = (2/5)·m·r²

p = %

Answer key

1. I_O = 10.92 kg·m²
2. E_k = 561 kJ
3. P = 197.9 kW
4. ω = 4.289 rad/s
5. ω = 7.659 rad/s
6. p = 28.57 %

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