Question

The angular acceleration of a rotating rigid body is given by α=(2.0−3.0t)rad/s². If the body starts rotating from rest at t=0,

(a) What is the angular velocity?
a) 2.0t− 3/2t² rad/s
b) 2.0t− 3.0t² rad/s
c) 2.0− 3.0t² rad/s
d) 2.0− 3/2t² rad/s
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Answer 1

The angular velocity of a rotating body with an angular acceleration of α = (2.0 - 3.0t) rad/s², starting from rest, is ω(t) = (2.0t - 1.5t²) rad/s.

Step-by-step explanation:

The question given involves a rigid body in rotational motion, and you are specifically asked to find the angular velocity given an angular acceleration that varies with time. The angular velocity is found by integrating the angular acceleration equation. The angular acceleration α is given by (2.0 - 3.0t) rad/s². Since the body starts from rest, initial angular velocity (ω_0) is 0 rad/s. The angular velocity ω(t) at time t can be found by integrating the acceleration function with respect to time:

ω(t) = ∫ α dt = ∫ (2.0 - 3.0t) dt = (2.0t - \frac{3}{2}t²) + C

Where C is the constant of integration. As the body starts from rest, ω(0) = 0, and thus C = 0.

The angular velocity is therefore ω(t) = (2.0t - \frac{3}{2}t²) rad/s, which corresponds to option (a).