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--V 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, = wt +at? Substitute the known values 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 t find the number revolutions: = A0 (1 revy 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: ",-a + at = rad/s Finalize We could also obtain this result using the equation w = 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

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--V 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, = wt +at? Substitute the known values 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 t find the number revolutions: = A0 (1 revy 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: ",-a + at = rad/s Finalize We could also obtain this result using the equation w = 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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