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 260 kg has a radius of gyration of 0.6 m about its axis. It spins at 1000 rpm. Find its kinetic energy E_k in kJ.

M = 260 kgk = 0.6 mn = 1000 rpm

E_k = kJ

2.Easy

A pendulum is made of a uniform slender rod (3.5 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 2.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.75 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 3.5 kgL = 1.5 mm_disc = 2.5 kgr = 0.25 md = 1.75 m

I_O = kg·m²

3.Medium

A shaft transmits 82 kW at 1700 rpm. Find the torque T in the shaft.

P = 82 kWn = 1700 rpm

T = N·m

4.Medium

A flywheel with a moment of inertia of 28 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 20 N·m. How many revolutions N does the flywheel make before it stops?

I = 28 kg·m²n = 2300 rpmT_b = 20 N·m

N = rev

5.Hard

A thin hoop of mass 1.5 kg rolls without slipping at 2 m/s. Find its total kinetic energy E_k.

m = 1.5 kgv = 2 m/sI = m·r²

E_k = J

6.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 4 m along the slope.

θ = 40°s = 4 mI = ½·m·r²g = 9.81 m/s²r = 0.05 m

ω = rad/s

Answer key

1. E_k = 513.2 kJ
2. I_O = 10.36 kg·m²
3. T = 460.6 N·m
4. N = 6463 rev
5. E_k = 6 J
6. ω = 116 rad/s

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