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my is question if this and i solve this question bu i am not getting he answer please solve my problem Q.A WHEEL ROTATES SO THE ANGLE OF ROTATION IS PROPORTIONAL TO THE SQUARE OF TIME THE FIRST REVOLUTION WAS PERFORMED BY THE WHEEL FOR 8 SECONDS.FIND THE ANGULAR VELOCITY Ω,32 SECOND AFTER THE WHEEL STARTING?

my is question if this and i solve this question bu i am not getting he answer please solve my problem  
Q.A WHEEL ROTATES SO THE ANGLE OF ROTATION IS PROPORTIONAL TO THE SQUARE OF TIME THE FIRST REVOLUTION WAS PERFORMED BY THE WHEEL FOR 8 SECONDS.FIND THE ANGULAR VELOCITY  Ω,32 SECOND AFTER THE WHEEL STARTING?

Grade:11

1 Answers

Arun
25763 Points
2 years ago
Dear Abhay
 
As the wheel rotates one time, it rotates an angle of 2 π radians. Use the following equation to determine the angular acceleration. 

θ = ωi * t + ½ * α * t^2, ωi = 0 
2 π = ½ * α * 8^2 
32 * α = 2 π 
α = 0.0625 * π 

This is approximately 0.2 rad/s^2. Use the following equation to determine the angular velocity at 32 seconds. 

ωf = ωi + α * t, ωi = 0 
ωf = 0.0625 * π * 32 = 2 π rad/s 
This is approximately 6.28 rad/s.

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