Two Rotational Motion Questions

  1. The first one:
    1. The problem statement, all variables and given/known data

    1) A compact disc (CD) stores music in a coded pattern of tiny pits 10^-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm , respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.

    2. Relevant equations

    alpha_avg = (omega_2 - omega_1) / (t2 - t1)
    omega_inner = 50.0 rad/s
    omega_outer = 21.6 rad/s

    3. The attempt at a solution

    I tried to take the average of the inner and outer angular velocities, and put that in for omega_2, and find the average that way, but I don't think I can do that.

    The second one:
    1. The problem statement, all variables and given/known data

    2) At t = 0 a grinding wheel has an angular velocity of 27.0 rad/s. It has a constant angular acceleration of 26.0 rad/s^2 until a circuit breaker trips at time t = 2.00 s. From then on, it turns through an angle 433 rad as it coasts to a stop at constant angular acceleration. At what time did it stop?

    2. Relevant equations

    omega_2 = omega_1 + alpha * t
    delta_2 - delta_1 = omega_1 * t + 0.5 * alpha * t^2

    3. The attempt at a solution

    I tried using a system of equations using the two equations above to solve for t, but I can't seem to get the right t value.

    Any guidance is greatly appreciated on either problem. Thanks in advance.
  2. jcsd
  3. learningphysics

    learningphysics 4,124
    Homework Helper

    For the first problem, your omega_inner and omega_outer look good to me. Why not just take (omega_outer - omega_inner)/(74*60)... that should be the answer.

    For the second problem, think of the angular velocity and acceleration, just like kinematics formulas...

    What is the angular velocity at t = 2?

    Then you can use the equation,

    angle traversed = [(omega_1 + omega_2)/2]*t, so solve for how long it takes to go through the 433 rad...
  4. Ok, thanks so much for your help. It makes more sense this way, than the way I initially tried to tackle the problems.
    Thanks again :)
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