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 7.5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 7.5 kgL = 2.7 md = 0.5 m

I_O = kg·m²

2.Easy

A pendulum is made of a uniform slender rod (3 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.55 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 3 kgL = 0.4 mm_sphere = 9 kgr = 0.15 md = 0.55 m

I_O = kg·m²

3.Medium

A uniform slender rod of mass 5.5 kg and length 0.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 5.5 kgL = 0.7 mg = 9.81 m/s²

R = N

4.Medium

A shaft transmits 74 kW at 2300 rpm. Find the torque T in the shaft.

P = 74 kWn = 2300 rpm

T = N·m

5.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7 m along the slope.

θ = 20°s = 7 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A solid sphere of mass 6.5 kg rolls without slipping at 3 m/s. Find its rotational kinetic energy E_rot.

m = 6.5 kgv = 3 m/sI = (2/5)·m·r²

E_rot = J

Answer key

1. I_O = 6.431 kg·m²
2. I_O = 2.964 kg·m²
3. R = 13.49 N
4. T = 307.2 N·m
5. v = 5.309 m/s
6. E_rot = 11.7 J

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