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 0.3 m is accelerated uniformly from rest to 600 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.3 mn₁ = 0 rpmn₂ = 600 rpmt = 28 s

T = N·m

2.Easy

A flywheel of mass 290 kg has a radius of gyration of 0.15 m about its axis. It spins at 2100 rpm. Find its kinetic energy E_k in kJ.

M = 290 kgk = 0.15 mn = 2100 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 10.5 kg and length 1.2 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 = 10.5 kgL = 1.2 mg = 9.81 m/s²

α = rad/s²

4.Medium

A shaft transmits 164 kW at 2600 rpm. Find the torque T in the shaft.

P = 164 kWn = 2600 rpm

T = N·m

5.Hard

A uniform solid disc (mass 7 kg, radius 0.2 m) spins freely at 900 rpm about a vertical frictionless shaft. A thin ring of mass 13 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n₂ in rpm.

M_disc = 7 kgM_ring = 13 kgR = 0.2 mn₁ = 900 rpm

n₂ = rpm

6.Hard

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 25°I = m·r²g = 9.81 m/s²

μ_s =

Answer key

1. T = 6.059 N·m
2. E_k = 157.8 kJ
3. α = 12.26 rad/s²
4. T = 602.3 N·m
5. n₂ = 190.9 rpm
6. μ_s = 0.2332

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