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 of mass 30 kg with a radius of gyration of 0.45 m is accelerated uniformly from rest to 200 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.45 mn₁ = 0 rpmn₂ = 200 rpmt = 11 s

T = N·m

2.Easy

A flywheel is a uniform solid disc of mass 190 kg and radius 0.35 m. It spins at 800 rpm. Find its kinetic energy E_k in kJ.

M = 190 kgR = 0.35 mn = 800 rpm

E_k = kJ

3.Medium

A motor brings a flywheel with a moment of inertia of 18.5 kg·m² from rest up to 3000 rpm in 34 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 18.5 kg·m²n = 3000 rpmt = 34 s

P_avg = kW

4.Medium

A uniform slender rod of mass 11.5 kg and length 1 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 = 11.5 kgL = 1 mg = 9.81 m/s²

α = rad/s²

5.Hard

A hollow sphere of mass 17.5 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 17.5 kgv = 3 m/sI = (2/3)·m·r²

p = %

6.Hard

A thin hoop starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 2.5 m along the slope.

θ = 35°s = 2.5 mI = m·r²g = 9.81 m/s²r = 0.15 m

ω = rad/s

Answer key

1. T = 11.57 N·m
2. E_k = 40.84 kJ
3. P_avg = 26.85 kW
4. α = 14.71 rad/s²
5. p = 40 %
6. ω = 25 rad/s

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