1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Disk falling while rotating round a point

  1. Aug 22, 2015 #1
    1. The problem statement, all variables and given/known data
    The disk of mass m and radius R is at position (a), upwards. it is free to rotate round point O on it's circumference.
    If falls and reaches state (b), horizontal position.
    What are the velocities and accelerations in position (b)

    2. Relevant equations
    Moment of inertia of a disk: ##I=\frac{1}{2}mR^2##
    Torque of rigid body: ##M=I\alpha##
    Energy of a rigid body: ##E=\frac{1}{2}I\omega^2##
    Centripetal acceleration: ##a_{cen}=\frac{v^2}{R}=\omega^2 R##

    3. The attempt at a solution
    The angular velocity ω is from energy conservation:
    $$mgR=mR^2\left( \frac{1}{2}+1 \right)\omega^2\; \rightarrow \omega^2=\frac{4g}{3R}$$
    COM's velocity is ##v_{cm}=\omega R=\sqrt{\frac{4g}{3R}}R=2\sqrt{\frac{gR}{3}}##
    The radial velocity from the circular motion:
    $$a_{cen}=\omega^2 R=\frac{4g}{3}$$
    Tangential acceleration is from the gravity:
    $$M=I\alpha\rightarrow mgR=\frac{3}{2}mR^2\alpha\rightarrow\alpha=\frac{2g}{3R}$$
    $$a_{tan}=R\alpha=\frac{2g}{3}$$
     

    Attached Files:

  2. jcsd
  3. Aug 22, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Looks right.
     
  4. Aug 22, 2015 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    One typo.... where you wrote radial velocity you meant radial acceleration.
     
  5. Aug 22, 2015 #4
    Thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Disk falling while rotating round a point
  1. Rotating Disk (Replies: 6)

  2. Rotating Disk (Replies: 2)

Loading...