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 7 kg and length 0.7 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 7 kgL = 0.7 md = 0.35 m

I_O = kg·m²

2.Easy

A uniform slender rod of mass 2.5 kg and length 1.7 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 2.5 kgL = 1.7 md = 0.3 m

I_O = kg·m²

3.Medium

A motor delivers a torque of 1620 N·m at 2800 rpm. Find its power output P in kW.

T = 1620 N·mn = 2800 rpm

P = kW

4.Medium

A shaft transmits 14.5 kW at 700 rpm. Find the torque T in the shaft.

P = 14.5 kWn = 700 rpm

T = N·m

5.Hard

A uniform slender rod of mass 7 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 580 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 = 7 kgL = 0.7 mm = 50 gv = 580 m/sd = 0.28 m

ω = rad/s

6.Hard

A solid cylinder rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9 m down the slope?

θ = 10°I = ½·m·r²g = 9.81 m/s²s = 9 m

t = s

Answer key

1. I_O = 1.143 kg·m²
2. I_O = 0.8271 kg·m²
3. P = 475 kW
4. T = 197.8 N·m
5. ω = 7.078 rad/s
6. t = 3.981 s

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