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 uniform slender rod of mass 10 kg and length 1.1 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 10 kgL = 1.1 md = 0.15 m

I_O = kg·m²

2.Easy

A pendulum is made of a uniform slender rod (4 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.95 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 4 kgL = 0.8 mm_sphere = 8 kgr = 0.15 md = 0.95 m

I_O = kg·m²

3.Medium

A flywheel with a moment of inertia of 31 kg·m² spins at 800 rpm. A brake applies a constant friction torque of 160 N·m. How long t does it take to stop?

I = 31 kg·m²n = 800 rpmT_b = 160 N·m

t = s

4.Medium

A shaft transmits 12 kW at 1000 rpm. Find the torque T in the shaft.

P = 12 kWn = 1000 rpm

T = N·m

5.Hard

A hollow sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 15°I = (2/3)·m·r²g = 9.81 m/s²

a = m/s²

6.Hard

A solid sphere of mass 10 kg rolls without slipping at 7 m/s. What percentage p of its total kinetic energy is rotational?

m = 10 kgv = 7 m/sI = (2/5)·m·r²

p = %

Answer key

1. I_O = 1.233 kg·m²
2. I_O = 8.145 kg·m²
3. t = 16.23 s
4. T = 114.6 N·m
5. a = 1.523 m/s²
6. p = 28.57 %

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