Question

Using the formula for kinetic energy of a moving particle k=12mv2, find the kinetic energy ka of particle a and the kinetic energy kb of particle
b. remember that both particles rotate about the y axis.

Answer 1

Answer: KE = (11/2)mω²r², particle B must have mass of 2m, while A has mass m. Then the moment of inertia of the system is I = Σ md² = m*(3r)² + 2m*r² = 11mr² and then KE = ½Iω² = ½ * 11mr² * ω² = 11mr²ω² / 2 So I'll proceed under that assumption. For particle A, translational KEa = ½mv² but v = ω*d = ω*3r, so KEa = ½m(3ωr)² = (9/2)mω²r² For particld B, translational KEb = ½(2m)v² but v = ω*r, so KEb = ½(2m)ω²r² so total translational KE = (9/2 + 2/2)mω²r² = 11mω²r² / 2 which is equal to our rotational KE.