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 = 0.35 mn = 2500 rpm260 kg

A flywheel of mass 260 kg has a radius of gyration of 0.35 m about its axis. It spins at 2500 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgk = 0.35 mn = 2500 rpm
Ek = kJ
2.Easy
Or = 0.15 mL = 0.7 m0.85 m0.5 kg4.5 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.7 mmsphere = 4.5 kgr = 0.15 md = 0.85 m
IO = kg·m²
3.Medium
n = 2500 rpmT = 1860 N·m

A motor delivers a torque of 1860 N·m at 2500 rpm. Find its power output P in kW.

T = 1860 N·mn = 2500 rpm
P = kW
4.Medium
L = 2.8 mm = 17 kgα

A uniform slender rod of mass 17 kg and length 2.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 17 kgL = 2.8 mg = 9.81 m/s²
R = N
5.Hard
disc: 2 kgring: 3 kgn1​ = 950 rpm

A uniform solid disc (mass 2 kg, radius 0.2 m) spins freely at 950 rpm about a vertical frictionless shaft. A thin ring of mass 3 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 = 2 kgMring = 3 kgR = 0.2 mn1 = 950 rpm
n2 = rpm
6.Hard
0.8 m0.35 mn1​ = 30 rpm

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 30 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 1 kgr1 = 0.8 mr2 = 0.35 mn1 = 30 rpm
n2 = rpm

Answer key

  1. 1. Ek = 1091 kJ
  2. 2. IO = 3.373 kg·m²
  3. 3. P = 486.9 kW
  4. 4. R = 41.69 N
  5. 5. n2 = 237.5 rpm
  6. 6. n2 = 35.92 rpm

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