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Rotational Motion and speed of a disc

  1. Jun 22, 2012 #1
    A 36.5-cm diameter disk rotates with a constant angular acceleration of 2.00 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.

    (a) Find the angular speed of the wheel at t = 2.30 s.
    (b) Find the linear velocity and tangential acceleration of P at t = 2.30 s.
    (c) Find the position of P (in degrees, with respect to the positive x-axis) at t = 2.30s.

    (a) to solve for angular speed W=at or W=(2)(2.3) and got 4.6m/s

    (b) first I calculated the radius by multiplying 36.5*.01 then dividing by 2 and got .1825.

    next I plugged it into V=(.1825)(4.6) to solve for linear velocity and got .8395.

    To get tangential acceleration I used A=(.1825)(2) and got .365.

    (c) θ=1+.5(2)(2.3)^2 and got 6.29 radians which I converted to degrees and got 360.39 and subtracted 360 to get position with respect to positive x-axis.

    Not sure If I did part this right can I get some verification??
     
  2. jcsd
  3. Jun 22, 2012 #2
    Well ..... why u added 1 to θ in the (c) part ?
    the formula simply says-
    θ=ωot + αt2
    and ωo is initial rotational velocity.... and since disk was at rest at t=0 so ωo = 0
    rest all is correct.
     
  4. Jun 22, 2012 #3
    The reason I did that in part c was because I subtracted θo to the right side of the equation. I thought the initial angular displacement would be 1 since it is one radian.
     
  5. Jun 22, 2012 #4
    I meant I added it to the right side of the equation oops
     
  6. Jun 22, 2012 #5
    ...... sorry ..... yes .... you are correct .
    even i meant Δθ by θ.
    and yes .... your answer is correct.
     
  7. Jun 22, 2012 #6
    ok thanks
     
  8. Jun 23, 2012 #7
    yes .... but the direction of angular acceleration will make a difference, if its clockwise or anticlockwise, the final angle with the x-axis would be different in the two cases.
     
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