Friday, February 17, 2006

Acceleration of the rim of a wheel

Radial and Tangential Acceleration

A wheel (radius r), starting from rest undergoes a uniform angular acceleration of alpha about its fixed axle. What are the tangential and radial accelerations as a function of alpha, r and t. Also, show that the angle between the total acceleration vector at P on the edge of the wheel and the radial vector is inversely proportional to the number of revolutions the wheel has made.


    atangential= alpha r

    aradial=acentripetal=omega2 r=(alpha t)2r

b) Let theta be the angle between the vector a and P and N the number of rotations (a real number, so it includes partial rotations).

    Tan(theta)=atangential/aradial=alphar/(alpha t)2r

    Tan(theta)=1/(alpha t)2


    alpha t2=2 omega =2*theta

    omega=2 pi N


Tan(theta)=1/4 pi N

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