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Angular motion, Work

  1. Dec 5, 2007 #1
    1. A rigid body, starting at rest, rotates about a fixed axis with a constant angular acceleration α. Consider a particle a distance r from the axis. Express (a) the radial acceleration and (b) the tangential acceleration of this particle in terms of α, r and time t.
    c) if the resultant acceleration of the particle at some instant makes an angle of 57.0 degrees with the tangential acceleration, through what total angle has the body rotated from t=0 to that instant.

    i got radial acceleration = rω^2 = (α^2)(t^2)r
    tangential acceleration = αr

    for c i made a triangle and got cos(57deg) = cos(.99rad) = (α^2)(t^2)r/αr = αt^2

    so i plugged it into the kinematics formula
    theta = (1/2)αt^2
    theta = (1/2)cos(.99rad)
    theta = .27 radians
    but that is incorrect

    2. Two particles, each with mass m, are fastened to each other and to a rotation axis by two rods, each with length L and mass M. The combination rotates around the rotation axis with angular velocity ω. Obtain an algebraic expression for the rotational inertia of the combination about the axis.

    I = m1r1^2 + m2r2^2
    I = ML^2 + M(2L)^2
    I = 5ML^2
    im not sure any other way to solve this

    3. A 52.3-kg trunk is pushed 5.95m at constant speed up a 28.0 degree incline by a constant horizontal force. The coefficient of kinetic friction between the trunk and the incline is .19 . Calculate the work done by a) the applied force and b) the force of gravity.

    I found the forge of gravity one easily, just mgh

    for a) I figured I should make my axes line up with the slope so
    Sum of forces in x = Fcos28 - f - mgsin28 = 0
    and then solving for F

    thanks
     
  2. jcsd
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