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Rotation of a Rigid Object About a Fixed Axis

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data
    A small object with mass 4.00kg moves counterclockwise with constant speed 4.50m/s in a circle of radius 3.00m centered at the origin. It starts at the point with position vector (3.00i+0j)m. Then it undergoes an angular displacement of 9.00rad. (a.) What it is position vector? Use unit-vector notation for all vector answers. (b.) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c.)What is its velocity? (d.)In what direction is it moving? Make a sketch of its position, velocity, and acceleration vectors. (e.) What is its acceleration? (f.) What total force is exerted on the object?

    m=4.00kg
    V=4.50m/s
    r=3.00m

    This is just a scary problem!


    2. Relevant equations
    I was told to break it down into the x and y components, but how do you know to do that?
    V=x/t
    To find the direction it is moving, we would use the right hand rule, right?
    a=V/t
    ƩF=ma


    3. The attempt at a solution
    I need to break it into x and y components, but I am lost on how to do that.
     
  2. jcsd
  3. Oct 25, 2011 #2
    Essentially you are given a problem in mixed coordinates, the initial position is (x,y) but the parameters of the problem are polar coordinates (r,θ). I would suggest it will be simpler to solve the motion in the polar coordinates since the radius is fixed. You therefore need to define how your polar coordinates will look, for instants you could define that θ=0 when the position vector from the origin points along the x axis.

    Then define your initial position vector, and follow the steps it gives you on how it moves.

    The best thing you can do is draw a really nice diagram. This will solve most of the problems.
     
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