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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 wheel rotating with uniform angular acceleration completes 50...

A wheel rotating with uniform angular acceleration completes 5050 revolutions in the first five seconds after starting. Determine the angular acceleration and the angular velocity at the end of five seconds.

Options

  1. A4 rev/s2, 20 rev/s4 \text{ rev/s}^2,\ 20 \text{ rev/s}
  2. B2 rev/s2, 10 rev/s2 \text{ rev/s}^2,\ 10 \text{ rev/s}
  3. C8 rev/s2, 40 rev/s8 \text{ rev/s}^2,\ 40 \text{ rev/s}
  4. D4 rev/s2, 10 rev/s4 \text{ rev/s}^2,\ 10 \text{ rev/s}

Correct answer

A. 4 rev/s2, 20 rev/s4 \text{ rev/s}^2,\ 20 \text{ rev/s}

Step-by-step solution

Given initial angular velocity ω0=0\omega_0 = 0, angular displacement θ=50 rev\theta = 50 \text{ rev}, and time t=5 st = 5 \text{ s}.

Using the second equation of rotational motion:

θ=ω0t+12αt2\theta = \omega_0 t + \dfrac{1}{2} \alpha t^2

50=0+12α(5)250 = 0 + \dfrac{1}{2} \alpha (5)^2

50=252α50 = \dfrac{25}{2} \alpha

α=10025=4 rev/s2\alpha = \dfrac{100}{25} = 4 \text{ rev/s}^2

Using the first equation of rotational motion to find the angular velocity at t=5 st = 5 \text{ s}:

ω=ω0+αt\omega = \omega_0 + \alpha t

ω=0+4×5=20 rev/s\omega = 0 + 4 \times 5 = 20 \text{ rev/s}
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