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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 9 / Problem 4E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Answer: CALC A fan blade rotates with angular velocity

Chapter 9, Problem 4E

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QUESTION:

Problem 4E

CALC A fan blade rotates with angular velocity given by ωz(t) = γ - βt2, where γ = 5.00 rad/s and β = 0.800 rad/s3. (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration αz at t = 3.00 s and the average angular acceleration αav-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?

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QUESTION:

Problem 4E

CALC A fan blade rotates with angular velocity given by ωz(t) = γ - βt2, where γ = 5.00 rad/s and β = 0.800 rad/s3. (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration αz at t = 3.00 s and the average angular acceleration αav-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?

ANSWER:

Solution 4E

Step 1:

(a).We know that the angular acceleration can be obtained from the angular velocity by taking derivative with respect to time of the angular velocity function.

$\alpha{}(t)=d{w}_{z}/dt=-2\beta{}t$

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