Problem 2. A flywheel with a radius of 0.25 m starts from rest and accelerates w

Question

Problem 2. A flywheel with a radius of 0.25 m starts from rest and accelerates with a constant angular acceleration of 1.00 rad/s2 about a horizontal axis through its center. (a) Compute the magnitudes of the radial (or centripetal) acceleration, the tangential acceleration, and the total acceleration for a point on its rnim 1 sec after the flywheel begins rotating. (b) What is the angle between the total acceleration and the radial acceleration? (c) What is the angular momentum about the flywheel about the axis of rotation at t-2.0 seconds?

Explanation / Answer

a) A total = sqroot ( Ar^2 + At^2)

Ar = radial acceleration = v^2/ R = ( w^2R^2/r) = w^2R = ( 1 rad/sec)^2 (0.25) = 0.25 rad/s^2

At= 0,25 (1) = 0.25

Atotal = 0.25 sqroot 2=0.353 rad/s^2

angle = tan^-1 (0.25/ 0,353) =35.3 degree apprx

L =Iw = ( 1/ 2mr^2)w =

I = momnet of inertia

w= 1( 2) = 2 rad/s

L = ( 1/2 ) ( M) (0.25^2) ( 2)

plug the value of mass and calculate the angular momnetum

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