Answer all questions please If the angular speed of the wheel is 2.75 rad/s at t

Question

Answer all questions please

If the angular speed of the wheel is 2.75 rad/s at t=0, through what angular displacement does the wheel rotate in 2.75 s? Conceptualize Imagine a compact disc rotates with its angular speed increasing at a constant rate. You start your stopwatch when the disc is rotating at 2.75 rad/s This mental image is a model for the motion of the wheel in this example. Categorize The phrase "with a constant angular acceleration" tells us to use the rigid object under constant angular acceleration model. Analyze Arrange the equation so that it at expresses the angular displacement of the object delta theta = theta _f- theta _i = omega _i t + 1/2 at^2 Substitute the known values to find the angular displacement at t=2.75 s in radians and degrees: delta theta = (2.75 rad/s)(2.75 s)+1/2 (4.00 rad/s^2)(2.75 s)^2 delta theta= (B) Through how many revolutions has the wheel turned during this time interval? Multiply the angular displacement found in part (A) by a conversion factor to find the number of revolutions: delta theta _rev= delta theta_deg (1 rev/360 degree) delta theta _rev (C) What is the angular speed of the wheel at t=2.75 s? Use the equation to find the angular speed at t=2.75 s omega _f= omega_i + alpha t =2.75 rad/s + 4.00 rad/s^2(2.75 s) Finalize We could also obtain this result using the equation omega_f^2= omega _i^2 + 2 alpha (theta _f- theta _i) and the results of part (A). through what angle does the wheel rotate between t=2.75 s and t=6.75 s?

Explanation / Answer

del theta = 22.68 degree ( 0.0174532925 radians/degree) = 0.39584067435 rad

del theta _ rev = 22.68 degree ( 0.00277777778 revolution/ degree) = 0.063 rev

wf = 13.75 rad/s

del theta = 13.75 ( 6.75-2.75) + 1/2 ( 4) ( ( 6.75-2.75)^2

=87 rad

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