The speed of a particle of mass m, moving in a circle of radius r, is changing at a constant rate aT m/ s2. Write the expression for the magnitude of its instantaneous resultant acceleration. Can we say that the direction of this instantaneous resultant acceleration would be along the instantaneous (inward) radial acceleration

Asked by pranayshah1908 | 28th Feb, 2021, 12:18: PM

Expert Answer:

If speed of particle moving in a circular path is chanigin at a constant rate  aT , then tangential acceleration = aT
 
Speed of particle v by assuming speed is 0 at t = 0 is given as
 
begin mathsize 14px style v space equals space a subscript T space cross times t end style
 
Radial acceleration, aR = v2 / R  
 
begin mathsize 14px style a subscript R space equals space a subscript T superscript 2 space cross times space t squared over R end style
 
where R is radius of circular path
 
Resultant instantaneous acceleration a  = begin mathsize 14px style square root of a subscript T superscript 2 plus a subscript R superscript 2 end root end style
begin mathsize 14px style a space equals space square root of fraction numerator a subscript T superscript 4 space t to the power of 4 over denominator R squared end fraction plus a subscript T superscript 2 end root space equals space a subscript T space square root of fraction numerator a subscript T superscript 2 space t to the power of 4 over denominator R squared end fraction plus space 1 end root end style
 
Instantaneous acceleration is not along the direction of radial accleration because radial acceleration and
tangential acceleration are perpendicular to each other.

Answered by Thiyagarajan K | 28th Feb, 2021, 03:04: PM

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