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. Alight 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 tangencial 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

a)inertia of disk is I = 1/2 mr2
and tension = I x a = inertia x angular acceleration
tangential acceleration = r x a = r x t/I = r x t / (1/2 mr2) = r x t x 2 / m / r2 = 2 t / r / m

b)I = 0.5*0.5*14.59*0.4*0.4*0.3048*0.3048 =0.054218214

T =2*4.44822 =8.89644

8.89644 = 0.054218214*a

angular acceleration =164.0858 m/sec^2

tangential acceleration =0.4*0.3048*164.0858 = 20.0053 m/sec^2

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