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A vinyl record player starts from rest and reaches a final angular velocity of 4pi rad s⁻¹ in 5 seconds. What is its angular acceleration?

Physics

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Answer

A) 0.8π rad s−2\text{A) } 0.8\pi \text{ rad s}^{-2}

Step-by-step solution

3 steps

A)

  1. Identify the given values.

    The initial angular velocity, since the record starts from rest, is ωi=0\omega_i = 0 rad s−1^{-1}.
    The final angular velocity is ωf=4π\omega_f = 4\pi rad s−1^{-1}.
    The time taken is t=5t = 5 s.

  2. Use the kinematic equation for angular motion.

    The relationship between initial angular velocity, final angular velocity, angular acceleration (α\alpha), and time is given by:

    ωf=ωi+αt\omega_f = \omega_i + \alpha t
  3. Substitute the given values into the equation and solve for α\alpha.

    4π rad s−1=0 rad s−1+α(5 s)4\pi \text{ rad s}^{-1} = 0 \text{ rad s}^{-1} + \alpha (5 \text{ s}) 4π=5α4\pi = 5\alpha α=4π5\alpha = \frac{4\pi}{5} α=0.8π rad s−2\alpha = 0.8\pi \text{ rad s}^{-2}

    The constant angular acceleration is 0.8π0.8\pi rad s−2^{-2}.

    The final answer is A) 0.8π rad s−2\text{A) } 0.8\pi \text{ rad s}^{-2}.

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