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A wheel starts from rest and accelerates uniformly at 2 rad/s2 for 5 seconds. What is its final angular velocity?

Physics

ScanSolve AI Answer

Answer

b\text{b}

Step-by-step solution

5 steps
  1. Identify the given values.

    The wheel starts from rest, so the initial angular velocity is ω0=0 rad/s\omega_0 = 0 \text{ rad/s}.
    The constant angular acceleration is α=2 rad/s2\alpha = 2 \text{ rad/s}^2.
    The time elapsed is t=5 st = 5 \text{ s}.

  2. Choose the appropriate kinematic equation for angular motion.

    To find the final angular velocity (ω\omega) given initial angular velocity, angular acceleration, and time, we use the equation:

    ω=ω0+αt\omega = \omega_0 + \alpha t
  3. Substitute the given values into the equation.

    ω=0 rad/s+(2 rad/s2)(5 s)\omega = 0 \text{ rad/s} + (2 \text{ rad/s}^2)(5 \text{ s})
  4. Calculate the final angular velocity.

    ω=0+10 rad/s\omega = 0 + 10 \text{ rad/s} ω=10 rad/s\omega = 10 \text{ rad/s}
  5. Compare the result with the given options.

    The calculated angular velocity is 10 rad/s10 \text{ rad/s}. This matches option b.

    The final answer is b\text{b}

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