A uniform disk of radius R and mass M is mounted on an axle supported in fixed f

Question

A uniform disk of radius R and mass M is mounted on an axle supported in fixed frictionless bearings. A light cord is wrapped around the rim of the wheel and a steady downward pull T is exerted on the cord. (a) Find the angular acceleration of the wheel and the tangential acceleration of a point on the rim. (first part, just write the equations), (b) then if the mass of disk is taken to be M = 0.50 slug, its radius is R = 0.40 ft, and the force is T = 2.0 lb, find the angular acceleration and tangential acceleration.

Explanation / Answer

T*R = I*alfa

alfa = T*R/I = (T*R)/((1/2)M*R^2

alfa = (2T)/MR

a = R*alfa = 2T/M

b) alfa = (2*2*4.448)/(0.5*14.59*0.4*0.3048)= 20.004 rad/s^2

a = R*alfa = 2.439 m/s^2

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