Expression Rolling
July 12th, 2011
Expression Rolling
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What is the algebraic expression for the magnitude α of the angular acceleration of the dragster's wheels? Exp
A dragster starts from rest and accelerates down the track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 374 m, the angular speed of the wheels is 276 rad/s.
What is the algebraic expression for the magnitude α of the angular acceleration of the dragster's wheels? Express your answer in terms of the dragster's initial and final linear speeds, v0 and v, the distance x it travels, and the radius r of a wheel.
w = angular acceleration
a = wr
x = v0t + (1/2)a t^2
x = v0t + (1/2)wr t^2
w (r t^2) = 2(x - v0t)
w(r t^2) + 2v0t = 2x
v = v0 + wrt
t = (v - v0)/wr
(v - v0)^2/wr + 2v0(v - v0)/wr = 2x
w = (1/(2xr))((v - v0)^2 + 2v0(v - v0))
w = (1/(2xr))(v - v0)( v - v0 + 2v0)
w = (1/(2xr))(v - v0)(v + v0)