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 = 0.4 m1000 → 1200 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.4 m is accelerated uniformly from 1000 rpm to 1200 rpm. This takes 13 s. Ignoring friction, find the constant torque T needed.

m = 70 kgk = 0.4 mn1 = 1000 rpmn2 = 1200 rpmt = 13 s
T = N·m
2.Easy
R = 0.55 mn = 500 rpm170 kg

A flywheel is a uniform solid disc of mass 170 kg and radius 0.55 m. It spins at 500 rpm. Find its kinetic energy Ek in kJ.

M = 170 kgR = 0.55 mn = 500 rpm
Ek = kJ
3.Medium
0 → 2500 rpmI = 21.5 kg·m²

A motor brings a flywheel with a moment of inertia of 21.5 kg·m² from rest up to 2500 rpm in 40 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 21.5 kg·m²n = 2500 rpmt = 40 s
Pavg = kW
4.Medium
v = ?2 kgL = 2.4 mm = 7 kg

A uniform slender rod of mass 7 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 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 kgL = 2.4 mmball = 2 kgg = 9.81 m/s²
v = m/s
5.Hard
θ = 40°as = 10 m

A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 10 m down the slope?

θ = 40°I = (2/5)·m·r²g = 9.81 m/s²s = 10 m
t = s
6.Hard
6 m/sω

A hollow sphere of mass 17.5 kg rolls without slipping at 6 m/s. Find its rotational kinetic energy Erot.

m = 17.5 kgv = 6 m/sI = (2/3)·m·r²
Erot = J

Answer key

  1. 1. T = 18.04 N·m
  2. 2. Ek = 35.25 kJ
  3. 3. Pavg = 18.42 kW
  4. 4. v = 7.731 m/s
  5. 5. t = 2.107 s
  6. 6. Erot = 210 J

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