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Transcribed Image Text:Rotating Wheel
A wheel rotates with a constant angular acceleration of 3.90 rad/s?.
(a) If the angular speed of the wheel is 2.52 rad/s at t, = 0, through what angular displacement does the wheel rotate in 2.00 s?
SOLUTION
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 2.52 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 apply the rigid object under
-Select---
angular acceleration model to the wheel.
Analyze
From the rigid object under constant acceleration model, rearrange the equation so that it expresses the angular displacement of the wheel:
A0 = 0,- 0, = ot +
Substitute the known values to find the angular displacement at t = 2.00 s. (Be sure your answer is in degrees.):
A0 =
(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:
1 rev
= A0
deg 360°
rev
rev
(c) What is the angular speed (in rad/s) of the wheel at t = 2.00 s?
Use the equation from the rigid object under constant angular acceleration model to find the angular speed at t = 2.00 s:
o,= 0, + at =
rad/s
2
Finalize We could also obtain this result using the equation w
+ 2a(0
-0) and the results of part (a). (Try it!)
EXERCISE
Through what angle (in rad) does the wheel rotate between t = 2.00 s and t = 6.00 s?
Hint
rad
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