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 5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 5 kgL = 2.3 md = 0.55 m

I_O = kg·m²

2.Easy

A pendulum is made of a uniform slender rod (4.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 7.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.45 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 4.5 kgL = 1.3 mm_disc = 7.5 kgr = 0.15 md = 1.45 m

I_O = kg·m²

3.Medium

A uniform slender rod of mass 7.5 kg and length 1.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 7.5 kgL = 1.3 mm_ball = 3 kgg = 9.81 m/s²

v = m/s

4.Medium

A motor delivers a torque of 930 N·m at 2600 rpm. Find its power output P in kW.

T = 930 N·mn = 2600 rpm

P = kW

5.Hard

A thin hoop of mass 4.5 kg rolls without slipping at 6.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 4.5 kgv = 6.5 m/sI = m·r²

p = %

6.Hard

A thin hoop of mass 5 kg rolls without slipping at 1 m/s. Find its total kinetic energy E_k.

m = 5 kgv = 1 m/sI = m·r²

E_k = J

Answer key

1. I_O = 3.717 kg·m²
2. I_O = 18.39 kg·m²
3. v = 5.595 m/s
4. P = 253.2 kW
5. p = 50 %
6. E_k = 5 J

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