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Linear and angular acceleration problems.

  1. Aug 29, 2013 #1
    1. The problem statement, all variables and given/known data

    A mass of 0.5kg is suspended from a flywheel. If the mass is released from rest and falls a distance of 0.5m in 1.5s. ( mass of wheel = 3kg, Radius = 0.3m, Radius of gyration = 212mm ).

    Calculate : a:The linear acceleration of the mass?
    b: The angular acceleration of the wheel?


    2. Relevant equations

    v=s/t
    a= v-u/t
    s=ut+1/2at^2

    3. The attempt at a solution

    I am getting conflicting answers to these questions. Heres my attempt!
    v = s/t so... v = 0.5/1.5 = 0.3333ms-1.
    Then...
    a = v-u/t so... v = 0.3333 - 0/1.5 = 0.2222ms-2

    So linear acceleration = 0.2222ms-2

    Question b : angular acceleration = acceleration/radius.

    so...

    angular acceleration = 0.2222/ 0.3 = 0.74 Rads-2.

    Now my linear acceleration is 0.222ms-2

    so if i put this answer into the equation s = ut + 1/2at^2. s should equal 0.5m. so..

    s = 1.5+1/2X0.2222x1.5^2 = 1.75s??? The answer should be 0.5m?

    Any help will be greatfully accepted.
     
  2. jcsd
  3. Aug 29, 2013 #2
    In your first equation you have not considered that there is acceleration so v is not s/t

    Edit: Also you have not considered that it begins from REST and falls 0.5m in 1.5s
     
  4. Aug 29, 2013 #3
    Average velocity = 0.5/1.5 = 0.3333ms

    So the distance from rest to fall = 0.5m so...

    0.333/0.5 = 0.6666ms.

    So velocity increases from 0 to 0.666ms in 1.5s.

    then: a= 0.6666/1.5 = 0.444ms-2 is the linear acceleration????
     
  5. Aug 29, 2013 #4
    No. You have acceleration so
    v = at
    s = 0.5at^2 are your equations
     
  6. Aug 29, 2013 #5
    third time lucky

    v = at

    a = v/t

    a = 0.3333/1.5 = 0.2222ms-1

    a = 0.2222ms-1 but distance is 0.5m so:

    0.2222/0.5 = 0.4444ms-2

    linear acceleration = 0.4444ms-2.

    checking with equation s = 0.5at^2

    s = 0.5x0.444x1.5^2 = 0.5m

    so inserting 0.4444 into the above equation gives me the correct distance. To my knowledge this tells me 0.4444ms-2 is correct??
     
  7. Aug 29, 2013 #6

    CAF123

    User Avatar
    Gold Member

    It is correct now. In your previous post, your 'a' had dimensions of 1/t2, so the answer before was coincidental.
     
  8. Aug 29, 2013 #7
    Well done. I think you are on your start doing physics. Try making good shapes and for every body you study draw the forces upon it so you can see how it will react. ;)
     
  9. Aug 29, 2013 #8
    Angular acceleration = acceleration/radius

    so

    0.444/0.3 = 1.48 rads-2

    This looks too simple to be correct!
     
  10. Aug 29, 2013 #9
    This is valid. Angular and linear velocities and accelerations are related simply with the radius
     
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