1. A cars wheels starts from rest and accelerate to 210 rpm in .73 seconds. a.)
ID: 1696132 • Letter: 1
Question
1. A cars wheels starts from rest and accelerate to 210 rpm in .73 seconds.a.) Find angular acceleration in radians/sec^2
b.) Find the revolutions completed in the time interval
c.) Find the total acceleration when it is 12m from the rotational axis at 180 rpm.
3. 1. a.) 210x2pi= radians/ min
1319.47/60= 21.99 radians/sec giving omega
21.99/.73= 30.12 radians/sec^2 giving angular acceleration. I think I did this right the whole revolution thing is throwing me for a loop.
b.) I think i just plug in everything into the formula W=Wo + at? If i do that, I get 0+30.12(.73)=21.99rad/sec
Then, I have to covert back to revolutions right? So, 21.99/2pi = 3.5 revolutions? Does that sound right?
c.) I know total acceleration is Centripetal plus tangential but after that I'm completely lost. Any help would be greatly appreciate I just don't get this. =/
Explanation / Answer
1) (a) Angular acceleration, = change in angular velocity / time = (210 rpm - 0 rpm) / t = 210 / 0.73 rpm/s = 287.67 * ( 2 Pi / 60 ) rad/s^2 = 30.12 rad/s^2 (b) Average angular velocity = [ 0 + 210 ( 2 Pi / 60 ) ] / 2 = 22 rad/s Angular displacement = Average angular velocity * time = 22 * 0.73 = 16.05 rad = 16.05 / 2 Pi = 2.6 rev (c) Centripetal acceleration, a1 = w^2 r = ( 180 * 2 Pi / 60 )^2 * 12 = 4263.66 m/s^2 Tangential acceleration, a2 = r * angular aceleration = 12 * [ 210 * ( 2 Pi / 60 ) - 0 ] / 0.73 = 361.5 m/s^2 Total acceleration, a = sqrt [ a1^2 + a2^2 ] = 4278.9 m/s^2
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