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 80 kg with a radius of gyration of 0.15 m is accelerated uniformly from 500 rpm to 2100 rpm. This takes 13 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.15 mn₁ = 500 rpmn₂ = 2100 rpmt = 13 s

T = N·m

2.Easy

A flywheel is a uniform solid disc of mass 120 kg and radius 0.45 m. It spins at 800 rpm. Find its kinetic energy E_k in kJ.

M = 120 kgR = 0.45 mn = 800 rpm

E_k = kJ

3.Medium

A shaft transmits 138 kW at 1500 rpm. Find the torque T in the shaft.

P = 138 kWn = 1500 rpm

T = N·m

4.Medium

A flywheel with a moment of inertia of 35.5 kg·m² spins at 2000 rpm. A brake applies a constant friction torque of 130 N·m. How many revolutions N does the flywheel make before it stops?

I = 35.5 kg·m²n = 2000 rpmT_b = 130 N·m

N = rev

5.Hard

A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 30°I = (2/5)·m·r²g = 9.81 m/s²

μ_s =

6.Hard

A hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9.5 m down the slope?

θ = 35°I = (2/3)·m·r²g = 9.81 m/s²s = 9.5 m

t = s

Answer key

1. T = 23.2 N·m
2. E_k = 42.64 kJ
3. T = 878.5 N·m
4. N = 953.2 rev
5. μ_s = 0.165
6. t = 2.372 s

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