- #1
lubo
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Homework Statement
A solid pulley wheel is rotated at a constant velocity for 10 sec's. Find the angular displacement?
Wo (inital angular velocity) = 6Rad/s
W (angular Velocity) = 0 Rads/s
[itex]\alpha[/itex] = 0 (angular acceleration) Rads/s-2
θ = ? (angular displacement) Rads/s
t = 10 sec
Homework Equations
θ=Wo*t+1/2*[itex]\alpha[/itex]*t squared
θ=(Wo+W)/2)*t
The Attempt at a Solution
θ=Wo*t+1/2*[itex]\alpha[/itex]*(t squared)
displacement θ = 6 * 10 + 1/2 * 0 * t = 60 Rads
or θ=(6+0)/2)*10 = 30 Rads.
I cannot tell which one is right as they both should find θ. All I know is that there is an angular acceleration of 0 and 60 is the right answer. Does this mean I have to use an equation with [itex]\alpha[/itex] in it?
I thought I could use anyone I liked as it found θ.
Another example is if I decelerate:
Wo = 6 Rads
[itex]\alpha[/itex] =-3Rads
t = 2 sec
θ=Wo*t+1/2*[itex]\alpha[/itex]*t squared
displacement θ = 6 * 2 + 1/2 * -3 * (2^2) = 6 Rads
or θ=(6+0)/2)*2 = 6 Rads.
Why would this work out or is it just luck? I know the answer to be 6 Rads.
Thank you for any help in advance.