A disc is having an initial angular velocity of 4 rad/sec and an angular acceleration of 8 rad/sec2. Find the angle rotated in radians by the disc in 3 sec. A. 48 rad B. 36 rad C. 12 rad D. 24 rad

The Correct answer is (A)

The equation of rotational motion for constant angular acceleration is given by

θ = ω_it + \(\frac{1}{2}\) αt²

Where, 

• θ = angular displacement of the body in time t
• ω_i = initial angular velocity
• α = angular acceleration

Given, 

Initial angular velocity, ω_i = 4 rad/s

Angular acceleration, α = 8 rad/sec²

Time, t = 3 sec

Using the equation of rotational motion, angular displacement (θ) of the disc in time (t), is given by 

θ = (4 x 3) + ( \(\frac{1}{2}\) x 8 x 3²)

⇒ θ = 12 + 36

⇒ θ = 48 rad.

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