Use the worked example above to help you solve this problem. A wheel rotates wit

Question

Use the worked example above to help you solve this problem. A wheel rotates with a constant angular acceleration of 3.05 rad/s^2. Assume the angular speed of the wheel is 1.90 rad/s at t_i = 0. Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions. What is the angular speed of the wheel at t = 2.00 s? What angular displacement (in revolutions) results while the angular speed found in part (b) doubles? Your response differs from the correct answer by more than 10%. Double check your calculations, Use the values from PRACTICE IT to help you work this exercise. Find the angle through which the wheel rotates between t = 2.00 s and t = 3.80 s. Find the angular speed when t = 3.80 s. What is the magnitude of the angular speed three revolutions following t = 3.80 s?

Explanation / Answer

(a)

use the equations which are the rotational analog of the general kinematics equations:

= t + 0.5t^2
= (1.90rad/s)(2s) + 0.5(3.05rad/s^2)(2s)^2
= 9.9rad

In revolutions:

9.9rad = 9.9 rad(1 rev / 2 rad)
= 1.58 rev

(b)

= + t
= 1.90 rad/s + (3.05 rad/s^2)(2s)
= 8 rad/s

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