How Does Uniform Angular Acceleration Affect Wheel Rotation Over Time?

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SUMMARY

The discussion focuses on calculating the angles rotated by a wheel subjected to uniform angular acceleration. Initially, the wheel has an angular velocity of zero and rotates 88.3 degrees in the first second. Using an angular acceleration of 1.54 degrees per second squared, the wheel rotates 264.64 degrees in the second second. The challenge remains in determining the angle for the third second, where the user is advised to apply the same angular acceleration formula with the appropriate time interval.

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  • Understanding of uniform angular acceleration
  • Familiarity with angular kinematics equations
  • Basic knowledge of calculus for manipulating equations
  • Ability to perform unit conversions (degrees to radians if necessary)
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  • Learn how to apply the angular kinematics equation: Change of Angle = Wi (change time) + 1/2(angular acceleration)(change time)^2
  • Explore the concept of angular acceleration and its implications in rotational motion
  • Investigate the relationship between angular displacement and time intervals in uniform acceleration scenarios
  • Practice problems involving multiple time intervals and uniform angular acceleration
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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.
 
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