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Rotational Kinematics of a disc

  1. Nov 8, 2009 #1
    How far has the disk moved?

    Disk has .34m radius with a mass of 7.4. The angular acceleration about the center of mass is 100.2 rad/s2.

    So this is what i did:
    ang. disp= .5(ang. accel)*t^2
    (x=.5(a)t^2 =>pretty much)

    I got my ang. disp to be 84.669 rad. Now i need to convert it to meters.
    The circum. of the circle i got was 2.136 (2(pi)r= 2*3.1415*.34). so thats how far it goes in 1 revolution.

    So i do 84.669rad* (1 rev/(2(pi) rad) * (2.136 m/ 1 rev)..... so (84.669*2.136)
    / (2(pi))

    I got the answer to be 28.78 m...and when i checked it was wrong...no idea where i went wrong

    Also the 2nd part of the question asks what is the translational speed of the disk... i have no idea what translational speed is or means. please help!!
     
  2. jcsd
  3. Nov 8, 2009 #2

    hage567

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    Homework Helper

    Were you given a value for time? Could you state the entire question as it was given to you?
     
  4. Nov 8, 2009 #3
    A solid uniform disk of mass M = 7.4 kg and radius R = 34 cm rests with its flat surface on a frictionless table (i.e., the axis of the cylinder is perpendicular to the table.) The diagram shows a top view. A string is wrapped around the rim of the disk and a constant force of F = 126 N is applied to the string. The string does not slip on the rim.

    a) What is the acceleration of the center of mass?
    a = m/s2 *
    17.03 OK

    HELP: Draw a free-body diagram and apply Newton's Second Law.

    b) What is the angular acceleration about the center of mass?
    a = rad/s2 *
    100.2 OK

    HELP: Draw a free-body diagram, find the torque, and apply the rotational analog of Newton's 2nd Law.

    The next 5 questions refer to a time 1.3 s after the force is first applied.
    c) How far has the disk moved?
    d = m
    28.783 NO

    HELP: This is a problem in one-dimensional kinematics.
    HELP: We have a constant acceleration, so we can use our standard kinematics formulas to find out the distance traveled in a given time.

    d) Through what angle has the disk turned?
    q = rad *
    84.669 OK

    e) What is the translational speed of the disk?
     
  5. Nov 8, 2009 #4

    hage567

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    I think you are missing a factor of two somewhere.

    Translation in this case just means as it moves across the table.
     
  6. Nov 8, 2009 #5
    missing a factor of 2? i dont know... like the math seems right. Maybe i am off by a little bit due to rounding error?
     
  7. Nov 8, 2009 #6
    yes..where I= .5*m*r^2
     
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