Results 1 to 2 of 2

Math Help - Turntable - rotation?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Turntable - rotation?

    A horizontal turntable in the form of a uniform disc of mass 150 kg is mounted on a light, frictionless vertical axis at its centre. Two men of mass 75 kg stand at opposite ends of a diameter, and they and the turntable are at rest. The men then move round the table in the same direction and at the same constant speed. Calculate the angle they have turned through in space when they have made one complete circuit of the table?

    Answer:
    Spoiler:
    \frac{4\pi}{3}


    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2008
    From
    Melbourne Australia
    Posts
    210
    Thanks
    25
    Let \phi _{p} be the angle through which the people turn with respect to the laboratory.

    Let \phi _{d} be the angle through which the disk turns with respect to the laboratory.

    v_{p}=\frac{r \phi_p}{t} because speed is constant

    angular momentum of people p_{p}=mrv_{p}=2*75*r*v_{p}

    angular momentum of disk = - angular momentum of people

    p_{disk}=I \omega = \frac 1 2 150 r^2 \frac {\phi_d}{t}=-mrv_{p}=-2*75*r*v_{p}=-2*75*r*\frac{r \phi_p}{t}

    \therefore \phi_d=-2\phi_p

    Now at the completion of one revolution across the surface of the disk

    \phi_p-\phi_d=2\pi

    You now have two equations in two variables phi_d and phi_p so you can solve them. Though I get a different answer to your spoiler, perhaps I made a silly algebraic mistake above.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: January 14th 2012, 08:02 PM
  2. Rotation in 3d
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 30th 2011, 03:36 PM
  3. [SOLVED] Parachutist landing on a turntable
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: December 22nd 2010, 12:08 PM
  4. Ant on Turntable
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 20th 2009, 11:41 PM
  5. PDE - rotation
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 12th 2008, 03:18 PM

Search Tags


/mathhelpforum @mathhelpforum