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 190 kg with a radius of gyration of 0.5 m is accelerated uniformly from 600 rpm to 2300 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.5 mn₁ = 600 rpmn₂ = 2300 rpmt = 15 s

T = N·m

2.Easy

A pendulum is made of a uniform slender rod (2.5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.6 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 2.5 kgL = 1.4 mm_disc = 9 kgr = 0.2 md = 1.6 m

I_O = kg·m²

3.Medium

A flywheel with a moment of inertia of 7 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 140 N·m. How long t does it take to stop?

I = 7 kg·m²n = 2300 rpmT_b = 140 N·m

t = s

4.Medium

A flywheel with a moment of inertia of 12 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 170 N·m. How long t does it take to stop?

I = 12 kg·m²n = 2400 rpmT_b = 170 N·m

t = s

5.Hard

A solid cylinder of mass 10.5 kg rolls without slipping at 2 m/s. What percentage p of its total kinetic energy is rotational?

m = 10.5 kgv = 2 m/sI = ½·m·r²

p = %

6.Hard

A solid sphere of mass 13 kg rolls without slipping at 6 m/s. What percentage p of its total kinetic energy is rotational?

m = 13 kgv = 6 m/sI = (2/5)·m·r²

p = %

Answer key

1. T = 563.7 N·m
2. I_O = 24.85 kg·m²
3. t = 12.04 s
4. t = 17.74 s
5. p = 33.33 %
6. p = 28.57 %

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