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
R = 0.4 mn = 1800 rpm40 kg

A flywheel is a uniform solid disc of mass 40 kg and radius 0.4 m. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgR = 0.4 mn = 1800 rpm
Ek = kJ
2.Easy
Or = 0.25 mL = 1.1 m1.35 m1 kg7.5 kg

A pendulum is made of a uniform slender rod (1 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 7.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 1.1 mmdisc = 7.5 kgr = 0.25 md = 1.35 m
IO = kg·m²
3.Medium
v = ?1.5 kgL = 1.6 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 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 = 7.5 kgL = 1.6 mmball = 1.5 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 2200 rpmTb​ = 200 N·mI = 12.5 kg·m²

A flywheel with a moment of inertia of 12.5 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 200 N·m. How many revolutions N does the flywheel make before it stops?

I = 12.5 kg·m²n = 2200 rpmTb = 200 N·m
N = rev
5.Hard
θ = 25°as = 1 m

A solid cylinder rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 1 m down the slope?

θ = 25°I = ½·m·r²g = 9.81 m/s²s = 1 m
t = s
6.Hard
8.5 m/sω

A solid cylinder of mass 14 kg rolls without slipping at 8.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 14 kgv = 8.5 m/sI = ½·m·r²
p = %

Answer key

  1. 1. Ek = 56.85 kJ
  2. 2. IO = 14.31 kg·m²
  3. 3. v = 6.419 m/s
  4. 4. N = 264 rev
  5. 5. t = 0.8507 s
  6. 6. p = 33.33 %

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