Thanks in advance for you help! A flywheel with a diameter of 1 m is initially a

Question

Thanks in advance for you help!

A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure. What is the angular separation between the initial position of a fixed point on the rim of the flywheel and the point's position 8 s after the wheel starts rotating? (Be sure to give angular separation rather than total angular displacement.) The point starts its motion at theta = 0. Calculate the linear position 8 s after the wheel starts rotating. (Let the initial position of the point be 0.5 x^ .) m Calculate the linear velocity vector 8 s after the wheel starts rotating. (Enter the magnitude.) Calculate the tangential acceleration vector after the wheel starts rotating. (Enter the magnitude.) Sketch the linear position, velocity vector, and acceleration vector 8 s after the wheel starts rotating.

Explanation / Answer

area of -t vurve gives change in angular velocity

area =(0.1/3)t^3

as initial angular velocity is zero

angular displacement =(0.1/3)t^3 dt =(0.1/12)t^4

t is from 0 to 8

we get total angular displacement =34.13 rads =10 full rotations and 0.869 rads

hence angular displacement =0.869

b)s =r =0.869*1 =0.869 m

angular velocity =(0.1/3)t^3 =17.1 rad/s

hence v =wr =17.1 m/s.......as r =1

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