IIT JEE , AIEEE Forum - Physics , Mechanics

sunip_the_mini_mastermind

Q. A body travels in a elliptical path whose position vector is given by
r=acos

t i+bsin

t j.
     i,j denote unit vectors along X and Y axis...
     Find the radial acceleration of the particle?

sunip_the_mini_mastermind

can anybody give the answer............

sunip_the_mini_mastermind

is there nobody to give the answer

bhartibhanushali

r is an position vector of an point representing instanteneous displacement

hence take double derivative to find aacelaration

r=acos(wt) i +bsin(wt).j
f'(r)=-a sin (wt)*w +b cos(wt)*w
f"(r)=-acos(wt)*w*w -bsin(wt)*w*w
=-w^2[acos(wt) +b sin(wt)]
radial accelaration A =-rW^2

konichiwa2x

,

iitkgp_bipin

Good work konichiwa2x.

konichiwa2x

Quote from bhartibhanushali:

r is an position vector of an point representing instanteneous displacement
hence take double derivative to find aacelaration
r=acos(wt) i +bsin(wt).j
f'(r)=-a sin (wt)*w +b cos(wt)*w
f"(r)=-acos(wt)*w*w -bsin(wt)*w*w
=-w^2[acos(wt) +b sin(wt)]
radial accelaration A =-rW^2

bhartibanshauli, Please not that net acceleration

(which is what you have found) The question requires us to find the radial acceleration alone, which is given by

.

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