How Does Uniform Angular Acceleration Affect Wheel Rotation Over Time?

[adstroud]

Uniform Angular Acceleration please help :)

A wheel is subjected to uniform angular acceleration. Initially its angular velocity is zero. During the first 1-s time interval, it rotates through an angle of 88.3

Through what angle does it rotate during the next 1-s time interval? - I found the second 1-s time interval to rotate through an angle of 264.64 deg.

Through what angle during the third 1-s time interval? - I can't seem to figure the angle for this time interval

Ok So for the first part I found the angular acceleration to be 1.54 from the equation angular acceleration= (wf - wi)/change in time for the first angle change 88.3. I used this angular acceleration in the eqn. Change of Angle = Wi (change time) + 1/2(angular acceleration)(change time)^2 I plugged in 2 for the change in time here. I took that answer which was 352.94-88.3 to get final angle of 264.64. I don't know how to manipulate the angular acceleration for the third 1-s interval, but i believe for this one i plug in 3 for the time change... then subtract the angles from the first two intervals to get the final interval.

 

[belliott4488]

Why don't you try telling us what you've done so far and how you've done it? You'll get more help if you do that.

 

[Moetasim]

Great job on solving the first part! To find the angle for the third 1-s interval, you can use the same equation: Change of Angle = Wi (change time) + 1/2(angular acceleration)(change time)^2. But this time, you can plug in 3 for the change in time and the same angular acceleration of 1.54. Then, you can subtract the angles from the first two intervals (264.64 deg and 88.3 deg) to get the final angle for the third interval. So it would be 352.94 deg - (264.64 deg + 88.3 deg) = 0 deg. This means that the wheel did not rotate during the third interval, which makes sense since it reached its maximum velocity during the second interval and maintained that velocity for the third interval. I hope this helps!