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
Or = 0.05 mL = 1.2 m1.25 m3.5 kg4 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1.2 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 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1.2 mmsphere = 4 kgr = 0.05 md = 1.25 m
IO = kg·m²
2.Easy
Or = 0.25 mL = 0.4 m0.65 m4.5 kg3 kg

A pendulum is made of a uniform slender rod (4.5 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 3 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.65 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 0.4 mmsphere = 3 kgr = 0.25 md = 0.65 m
IO = kg·m²
3.Medium
n = 2500 rpmTb​ = 60 N·mI = 37.5 kg·m²

A flywheel with a moment of inertia of 37.5 kg·m² spins at 2500 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?

I = 37.5 kg·m²n = 2500 rpmTb = 60 N·m
t = s
4.Medium
n = 400 rpmTb​ = 20 N·mI = 29 kg·m²

A flywheel with a moment of inertia of 29 kg·m² spins at 400 rpm. A brake applies a constant friction torque of 20 N·m. How many revolutions N does the flywheel make before it stops?

I = 29 kg·m²n = 400 rpmTb = 20 N·m
N = rev
5.Hard
disc: 21 kgring: 18 kgn1​ = 350 rpm

A uniform solid disc (mass 21 kg, radius 0.2 m) spins freely at 350 rpm about a vertical frictionless shaft. A thin ring of mass 18 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 21 kgMring = 18 kgR = 0.2 mn1 = 350 rpm
n2 = rpm
6.Hard
θ = 40°vs = 1.5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 1.5 m along the slope.

θ = 40°s = 1.5 mI = m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. IO = 7.934 kg·m²
  2. 2. IO = 1.583 kg·m²
  3. 3. t = 163.6 s
  4. 4. N = 202.5 rev
  5. 5. n2 = 128.9 rpm
  6. 6. ω = 12.3 rad/s

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