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 is a uniform solid disc of mass 130 kg and radius 0.3 m. It spins at 2600 rpm. Find its kinetic energy E_k in kJ.

M = 130 kgR = 0.3 mn = 2600 rpm

E_k = kJ

2.Easy

A uniform slender rod of mass 2.5 kg and length 0.4 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 = 2.5 kgL = 0.4 md = 0.2 m

I_O = kg·m²

3.Medium

A motor delivers a torque of 1980 N·m at 2500 rpm. Find its power output P in kW.

T = 1980 N·mn = 2500 rpm

P = kW

4.Medium

A motor brings a flywheel with a moment of inertia of 20 kg·m² from rest up to 800 rpm in 47 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 20 kg·m²n = 800 rpmt = 47 s

P_avg = kW

5.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 8.5 m along the slope.

θ = 25°s = 8.5 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.15 m

ω = rad/s

6.Hard

A uniform slender rod of mass 6.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 5 g bullet moving horizontally at 500 m/s hits the rod 0.39 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 6.5 kgL = 0.6 mm = 5 gv = 500 m/sd = 0.39 m

ω = rad/s

Answer key

1. E_k = 216.8 kJ
2. I_O = 0.1333 kg·m²
3. P = 518.4 kW
4. P_avg = 1.493 kW
5. ω = 43.35 rad/s
6. ω = 1.249 rad/s

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