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 20 kg has a radius of gyration of 0.6 m about its axis. It spins at 2400 rpm. Find its kinetic energy E_k in kJ.

M = 20 kgk = 0.6 mn = 2400 rpm

E_k = kJ

2.Easy

A uniform slender rod of mass 6.5 kg and length 1.6 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 6.5 kgL = 1.6 md = 0.4 m

I_O = kg·m²

3.Medium

A flywheel with a moment of inertia of 26.5 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 170 N·m. How long t does it take to stop?

I = 26.5 kg·m²n = 300 rpmT_b = 170 N·m

t = s

4.Medium

A 9 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 9 kgM = 5.5 kgR = 0.25 mg = 9.81 m/s²

T = N

5.Hard

A solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 40°I = ½·m·r²g = 9.81 m/s²

a = m/s²

6.Hard

A hollow sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 20°I = (2/3)·m·r²g = 9.81 m/s²

μ_s =

Answer key

1. E_k = 227.4 kJ
2. I_O = 2.427 kg·m²
3. t = 4.897 s
4. T = 20.66 N
5. a = 4.204 m/s²
6. μ_s = 0.1456

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