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 kg and length 1.3 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 kgL = 1.3 md = 0.5 m

I_O = kg·m²

2.Easy

A pendulum is made of a uniform slender rod (4 kg, 1.1 m long) pivoted at its top end O, with a solid sphere of mass 4 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.15 m below O. Find the mass moment of inertia I_O of the pendulum about O.

m_rod = 4 kgL = 1.1 mm_sphere = 4 kgr = 0.05 md = 1.15 m

I_O = kg·m²

3.Medium

A uniform slender rod of mass 17 kg and length 1.7 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 = 17 kgL = 1.7 mg = 9.81 m/s²

R = N

4.Medium

A motor delivers a torque of 10 N·m at 900 rpm. Find its power output P in kW.

T = 10 N·mn = 900 rpm

P = kW

5.Hard

A thin hoop of mass 13 kg rolls without slipping at 10 m/s. Find its total kinetic energy E_k.

m = 13 kgv = 10 m/sI = m·r²

E_k = J

6.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 6 m along the slope.

θ = 15°s = 6 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. I_O = 2.736 kg·m²
2. I_O = 6.907 kg·m²
3. R = 41.69 N
4. P = 0.9425 kW
5. E_k = 1300 J
6. v = 4.276 m/s

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