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
L = 0.6 mGOd = 0.15 mm = 5 kg

A uniform slender rod of mass 5 kg and length 0.6 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 0.6 md = 0.15 m
IO = kg·m²
2.Easy
k = 0.35 m0 → 1900 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1900 rpm. This takes 26 s. Ignoring friction, find the constant torque T needed.

m = 180 kgk = 0.35 mn1 = 0 rpmn2 = 1900 rpmt = 26 s
T = N·m
3.Medium
v = ?4.5 kgL = 1.9 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 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 = 2.5 kgL = 1.9 mmball = 4.5 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 1900 rpmTb​ = 40 N·mI = 38.5 kg·m²

A flywheel with a moment of inertia of 38.5 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 40 N·m. How many revolutions N does the flywheel make before it stops?

I = 38.5 kg·m²n = 1900 rpmTb = 40 N·m
N = rev
5.Hard
θ = 10°vs = 8.5 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8.5 m along the slope.

θ = 10°s = 8.5 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
560 m/s30 g0.59 mL = 0.6 m5 kg

A uniform slender rod of mass 5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 560 m/s hits the rod 0.59 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 5 kgL = 0.6 mm = 30 gv = 560 m/sd = 0.59 m
ω = rad/s

Answer key

  1. 1. IO = 0.2625 kg·m²
  2. 2. T = 168.7 N·m
  3. 3. v = 6.34 m/s
  4. 4. N = 3032 rev
  5. 5. v = 4.168 m/s
  6. 6. ω = 16.24 rad/s

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