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 = 0.55 mn = 300 rpm280 kg

A flywheel of mass 280 kg has a radius of gyration of 0.55 m about its axis. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgk = 0.55 mn = 300 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.5 m0.7 m0.5 kg4.5 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.5 mmsphere = 4.5 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
n = 1500 rpmTb​ = 195 N·mI = 15.5 kg·m²

A flywheel with a moment of inertia of 15.5 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 195 N·m. How long t does it take to stop?

I = 15.5 kg·m²n = 1500 rpmTb = 195 N·m
t = s
4.Medium
n = 2000 rpmT = 1730 N·m

A motor delivers a torque of 1730 N·m at 2000 rpm. Find its power output P in kW.

T = 1730 N·mn = 2000 rpm
P = kW
5.Hard
disc: 12 kgring: 1 kgn1​ = 200 rpm

A uniform solid disc (mass 12 kg, radius 0.35 m) spins freely at 200 rpm about a vertical frictionless shaft. A thin ring of mass 1 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 12 kgMring = 1 kgR = 0.35 mn1 = 200 rpm
ΔE = J
6.Hard
0.6 m0.3 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 5 kgr1 = 0.6 mr2 = 0.3 mn1 = 25 rpm
n2 = rpm

Answer key

  1. 1. Ek = 41.8 kJ
  2. 2. IO = 2.319 kg·m²
  3. 3. t = 12.49 s
  4. 4. P = 362.3 kW
  5. 5. ΔE = 23.03 J
  6. 6. n2 = 36.44 rpm

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