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
k = 0.3 m400 → 2300 rpm50 kg

A flywheel of mass 50 kg with a radius of gyration of 0.3 m is accelerated uniformly from 400 rpm to 2300 rpm. This takes 7 s. Ignoring friction, find the constant torque T needed.

m = 50 kgk = 0.3 mn1 = 400 rpmn2 = 2300 rpmt = 7 s
T = N·m
2.Easy
Or = 0.15 mL = 1.4 m1.55 m4 kg9.5 kg

A pendulum is made of a uniform slender rod (4 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 1.4 mmsphere = 9.5 kgr = 0.15 md = 1.55 m
IO = kg·m²
3.Medium
n = 600 rpmTb​ = 120 N·mI = 25 kg·m²

A flywheel with a moment of inertia of 25 kg·m² spins at 600 rpm. A brake applies a constant friction torque of 120 N·m. How long t does it take to stop?

I = 25 kg·m²n = 600 rpmTb = 120 N·m
t = s
4.Medium
5.5 kgaαM = 15.5 kgR = 0.35 m

A 5.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 15.5 kg and radius 0.35 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 5.5 kgM = 15.5 kgR = 0.35 mg = 9.81 m/s²
a = m/s²
5.Hard
θ = 10°vs = 1 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 1 m along the slope.

θ = 10°s = 1 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s
6.Hard
3 m/sω

A solid cylinder of mass 10 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 10 kgv = 3 m/sI = ½·m·r²
p = %

Answer key

  1. 1. T = 127.9 N·m
  2. 2. IO = 25.52 kg·m²
  3. 3. t = 13.09 s
  4. 4. a = 4.072 m/s²
  5. 5. ω = 5.2 rad/s
  6. 6. p = 33.33 %

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