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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A body rotates about a fixed axis with an angular acceleration of...

A body rotates about a fixed axis with an angular acceleration of one radian/second/second\text{radian/second/second}. Determine the angle through which it rotates during the time in which its angular velocity increases from 5 rad/s5 \text{ rad/s} to 15 rad/s15 \text{ rad/s}.

Options

  1. A100 rad100 \text{ rad}
  2. B50 rad50 \text{ rad}
  3. C150 rad150 \text{ rad}
  4. D200 rad200 \text{ rad}

Correct answer

A. 100 rad100 \text{ rad}

Step-by-step solution

Using the third equation of rotational kinematics:

ωf2=ωi2+2αθ\omega_f^2 = \omega_i^2 + 2\alpha\theta

Given ωi=5 rad/s\omega_i = 5 \text{ rad/s}, ωf=15 rad/s\omega_f = 15 \text{ rad/s}, and α=1 rad/s2\alpha = 1 \text{ rad/s}^2.

Substituting the values into the equation:

(15)2=(5)2+2(1)θ(15)^2 = (5)^2 + 2(1)\theta

225=25+2θ225 = 25 + 2\theta

2θ=2002\theta = 200

θ=100 rad\theta = 100 \text{ rad}
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