order to determine the turbines initial angular velocity \u03d6 for part a However

# Order to determine the turbines initial angular

This preview shows page 13 - 15 out of 43 pages. 148ROTATIONAL KINEMATICS24.REASONINGThe angular displacement is given by Equation 8.6 as the product of the average angular velocity and the time(29102Average angularvelocityttθϖϖϖ==+1 42 43This value for the angular displacement is greater than ϖ0t. When the angular displacement θis given by the expression θ= ϖ0t, it is assumed that the angular velocity remains constant at its initial (and smallest) value of ϖ0for the entire time, which does not, however, account for the additional angular displacement that occurs because the angular velocity is increasing.The angular displacement is also less than ϖt. When the angular displacement is given by the expression θ= ϖt, it is assumed that the angular velocity remains constant at its final (and largest) value of ϖfor the entire time, which does not account for the fact that the wheel was rotating at a smaller angular velocity during the time interval.SOLUTIONa. If the angular velocity is constant and equals the initial angular velocity ϖ0, then ϖ= ϖ0 and the angular displacement is(29(290220 rad /s10.0 s2200 radtθϖ== +=+b. If the angular velocity is constant and equals the final angular velocity ϖ, then ϖ= ϖand the angular displacement is(29(29280 rad /s10.0 s2800 radtθϖ==+=+c. Using the definition of average angular velocity, we have(29(29(2911022220 rad /s + 280 rad /s10.0 s2500 radtθϖϖ=+=+=+(8.6)  #### You've reached the end of your free preview.

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• Spring '11
• rollino
• Physics, Angular velocity, Velocity, θ, rad/s, angular displacement
• • • 