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 70 kg has a radius of gyration of 0.5 m about its axis. It spins at 1500 rpm. Find its kinetic energy E_k in kJ.

M = 70 kgk = 0.5 mn = 1500 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 70 kg and radius 0.8 m. It spins at 1900 rpm. Find its kinetic energy E_k in kJ.

M = 70 kgR = 0.8 mn = 1900 rpm

E_k = kJ

3.Medium

An 8.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9 kg and radius 0.2 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 = 8.5 kgM = 9 kgR = 0.2 mg = 9.81 m/s²

T = N

4.Medium

A flywheel with a moment of inertia of 28.5 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 35 N·m. How many revolutions N does the flywheel make before it stops?

I = 28.5 kg·m²n = 1000 rpmT_b = 35 N·m

N = rev

5.Hard

A hollow sphere of mass 16.5 kg rolls without slipping at 2 m/s. Find its total kinetic energy E_k.

m = 16.5 kgv = 2 m/sI = (2/3)·m·r²

E_k = J

6.Hard

A thin hoop starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.4 m. Find its angular velocity ω after it has rolled 5.5 m along the slope.

θ = 30°s = 5.5 mI = m·r²g = 9.81 m/s²r = 0.4 m

ω = rad/s

Answer key

1. E_k = 215.9 kJ
2. E_k = 443.4 kJ
3. T = 28.86 N
4. N = 710.6 rev
5. E_k = 55 J
6. ω = 12.98 rad/s

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