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we only need to look at the equation for thex-position, since we know that centripetal acceleration points towards the center of the circle. Thus, when?= 0, the second derivative ofxwith respect to time must be the centripetal acceleration.The first derivative ofxwith respect to timetis:dx/dt= —Rsin?(d?/dt)The second derivative ofxwith respect to timetis:d2x/dt2= —Rcos?(d?/dt)2—Rsin?(d2?/dt2)In both of the above equations the chain rule of Calculus is used and by assumption?is a function of time. Therefore,?can be differentiated with respect to time.Now, evaluate the second derivative at?= 0.We have,d2x/dt2= —R(d?/dt)2The term d?/dtis usually called the angular velocity, which is the rate of change of the angle?. It has units of radians/second.For convenience we can setw= d?/dt.Therefore,d2x/dt2= —Rw2
this is centripital acceleration
sher mohammad
askiitian faculty
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