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 pendulum is made of a uniform slender rod (5 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.05 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 5 kgL = 0.9 mm_sphere = 5 kgr = 0.15 md = 1.05 m

I_O = kg·m²

2.Easy

A flywheel is a uniform solid disc of mass 60 kg and radius 0.65 m. It spins at 1900 rpm. Find its kinetic energy E_k in kJ.

M = 60 kgR = 0.65 mn = 1900 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 19.5 kg and length 2.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 19.5 kgL = 2.8 mg = 9.81 m/s²

α = rad/s²

4.Medium

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10 kg and radius 0.15 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 = 7.5 kgM = 10 kgR = 0.15 mg = 9.81 m/s²

T = N

5.Hard

A solid sphere of mass 6 kg rolls without slipping at 9 m/s. Find its total kinetic energy E_k.

m = 6 kgv = 9 m/sI = (2/5)·m·r²

E_k = J

6.Hard

A hollow sphere of mass 14.5 kg rolls without slipping at 9 m/s. What percentage p of its total kinetic energy is rotational?

m = 14.5 kgv = 9 m/sI = (2/3)·m·r²

p = %

Answer key

1. I_O = 6.907 kg·m²
2. E_k = 250.9 kJ
3. α = 5.255 rad/s²
4. T = 29.43 N
5. E_k = 340.2 J
6. p = 40 %

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