Hi, I want to find ds when s=alpha(angle)*R!
I thought that ds=d(alpha)*R+dR*alpha....and since R= constant, then dR=0!
so ds= d(alpha)*R.
However, my text book says ds=alpha(dot)*R.
I know that alpha(dot) is the derivate of alpha with respect to the time but is d(alpha) always alpha(dot)?
I thought that ds=d(alpha)*R+dR*alpha....and since R= constant, then dR=0!
so ds= d(alpha)*R.
However, my text book says ds=alpha(dot)*R.
I know that alpha(dot) is the derivate of alpha with respect to the time but is d(alpha) always alpha(dot)?
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You are correct. The book is wrong.
dα is not the same as α(dot).
α(dot) means dα/dt.
ds = dαR is correct (providing the motion is circular)
By the way, there is no such word as 'derivate'.
E.g. y = x²
If you differentiate y with respect to x, you get dy/dx = 2x.
dy/dx is called the derivative.
dα is not the same as α(dot).
α(dot) means dα/dt.
ds = dαR is correct (providing the motion is circular)
By the way, there is no such word as 'derivate'.
E.g. y = x²
If you differentiate y with respect to x, you get dy/dx = 2x.
dy/dx is called the derivative.