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 4.5 kg and length 2.9 m rotates about an axis O perpendicular to the rod, 1.2 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 4.5 kgL = 2.9 md = 1.2 m

I_O = kg·m²

2.Easy

A flywheel of mass 130 kg has a radius of gyration of 0.4 m about its axis. It spins at 3000 rpm. Find its kinetic energy E_k in kJ.

M = 130 kgk = 0.4 mn = 3000 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 11.5 kg·m² spins at 700 rpm. A brake applies a constant friction torque of 135 N·m. How long t does it take to stop?

I = 11.5 kg·m²n = 700 rpmT_b = 135 N·m

t = s

4.Medium

A uniform slender rod of mass 3 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 3 kgL = 0.6 mg = 9.81 m/s²

ω = rad/s

5.Hard

A solid sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8 m along the slope.

θ = 25°s = 8 mI = (2/5)·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A thin hoop rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 40°I = m·r²g = 9.81 m/s²

μ_s =

Answer key

1. I_O = 9.634 kg·m²
2. E_k = 1026 kJ
3. t = 6.244 s
4. ω = 7.004 rad/s
5. v = 6.883 m/s
6. μ_s = 0.4195

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