Tangential Acceleration vs. Tangential component of force

  1. 1. The problem statement, all variables and given/known data
    A ball moves counterclockwise in a circle and is speeding up. The radius of the circle is 5 m.

    Its angular acceleration is α, (2.09 rad/s2)[tex]\hat{k}[/tex]

    The ball's mass is 0.125 kg.

    What is the tangential component of the force on the particle?

    2. Relevant equations

    3. The attempt at a solution
    So the tangential acceleration is at = αr = 10.47 m/s2[tex]\hat{t}[/tex]

    (Define [tex]\hat{t}[/tex] to be tangent to the circle. At the top of the circle, it points to the left. At the bottom, it points to the right and so on).

    Then the tangential component of the FORCE on this particle should be (10.47 m/s2)[tex]\hat{t}[/tex] * 0.125 kg = (1.3 N)[tex]\hat{t}[/tex]

    But I got it wrong, and I have no clue why. Can anyone help me out? I got half the marks so it may just be a small error somewhere =\
    Last edited: Feb 14, 2010
  2. jcsd
  3. kuruman

    kuruman 3,449
    Homework Helper
    Gold Member

    The calculation looks OK. Components of vectors do not have unit vectors attached to them. Try without the t-hat.
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