Physics

A long thin rod of mass M = 2:00 kg and length L = 75:0 cm is free to rotate about its
center as shown. Two identical masses (each of mass m = .403 kg) slide
without friction along the rod. The two masses begin at the rod's point of rotation when
the rod is rotating at 10.0 rad/s.
(a) When they have moved halfway to the end of the rod, how fast (rad/s) is the rod
rotating?
(b) When the masses are halfway to the end of the rod, what is the ratio of the nal
kinetic energy to the initial kinetic energy (Kf=Ki)?
(c) When they reach the end, how fast is the rod rotating (rad/s)?

asked by Lindsay
  1. Use conservation of angular momentum.

    I*w = constant

    I is the moment of inertia, which is
    (1/12)Mrod*L^2 + 2m*R^2

    R is the distance of the masses from the center of the rod.

    w = 10.0 when R = 0

    For (a) and (b), R = L/4

    For (c), R = L/2

    Let's do (a)

    Angular momentum with massesw m at R=0:
    = (1/12)*2.00*(0.75)^2*10
    = 9.38*10^-1 kg m^2/s
    (This remains constant).
    When R = L/4 = 0.1875 m,
    I*w = (2/12)*(0.75)^2*w + 2*(0.403)*(0.1875)^2*w
    = (9.38*10^-2 + 2.83*10^-2)w
    = 1.221*10^-1*w = 9.38*10^-1
    w = 7.68 m/s

    For (b), compare initial and final values of (1/2) I w^2

    For (c), repeat the process of (a), but use R = L/2

    posted by drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A thin, rigid, uniform rod has a mass of 2.60 kg and a length of 1.69 m. (a) Find the moment of inertia of the rod relative to an axis that is perpendicular to the rod at one end.A thin, rigid, uniform rod has a mass of 2.60 kg
  2. physics

    A thin rod of mass M and length L is lying on a frictionless table. It is given an impulse of 4.5 N*s by a force of magnitude F on one end at an angle of 35 degrees to the rod. How far will the center of mass of the rod travel
  3. Physics - please help!!..

    A long thin rod lies along the x-axis from the origin to x=L, with L= 0.890 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x2). The value of λ0 is 0.700 kg/m and x is
  4. Physics

    A long thin rod lies along the x-axis from the origin to x=L, with L= 0.890 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x2). The value of λ0 is 0.700 kg/m and x is
  5. Physics

    A long thin rod lies along the x-axis from the origin to x=L, with L= 0.750 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x3). The value of λ0 is 0.600 kg/m and x is
  6. Physics

    A long thin rod lies along the x-axis from the origin to x=L, with L= 0.890 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x2). The value of λ0 is 0.700 kg/m and x is
  7. physics

    A long thin rod lies along the x-axis from the origin to x=L, with L= 0.890 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x2). The value of λ0 is 0.700 kg/m and x is
  8. Physics- Angular Momentum

    A long thin rod of mass M=2.00 kg and length L=75.0 cm is free to rotate about its center. Two identical masses (each of mass m = .45kg) slide without friction along the rod. The two masses begin at the rod's point of rotation
  9. rotational mechanics

    a thin rod of length 2R and mass M is standing vertically on a perfectly smooth floor. the state of equilibrium in which the rod at rest is unstable and the rod falls. FInd the trajectories that the various points of rod describe
  10. physics

    A thin non-uniform rod of length L=2.00 m and mass M=9.00 kg is free to pivot about an axis at one end. The CM of the rod is at a distance d=1.30 m from that end as illustrated below. The rod's moment of inertia about an axis

More Similar Questions