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Circular motion and angular speed

  1. Nov 14, 2006 #1
    [​IMG]

    A cylinder is rotating with angular speed
    -- take some points along radius and find if they have same angular speed ?
    ---- same tangential speed ?
    ------ same tangential acceleration ?


    I think that they will have will same angular speed becuase all the points on the cylinder are moving with same speed.
    But tangential speed would be different because it is the speed which is calculated at a specific point and each point will have different direction while moving.
    and for tangential acceleration .. each point would have different.


    Tell me if I am doing it right .
    Thanks
     
  2. jcsd
  3. Nov 14, 2006 #2

    OlderDan

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    You are correct about the angular speed; it is common to all points. The tangential speed is different for points that are different distances from the axis. Speed is not about direction. Speed is the magnitude of the velocity. All points along a given radius in the object are moving in the same direction but with different speeds. The same is true of the tangential acceleration. Tangential speed and acceleration are both proportional to the distance from the axis of rotation.
     
  4. Nov 14, 2006 #3
    Thanks

    what about the tangential veocity .... I think its the different as you told that the points at different distances would have different tangential velocity.
    is it rite ?
    I am very very confused about these terms :
    angular speed, angular velocity, tangential speed, tangential velocity, tangential acceleration and angular acceleration.

    I don't get that what's the main difference between them ? what do we spcifically look for ? (I mean distance from the axis or the angles, directions etc).
    Please if someone can clear this . I'll be really thankful to you.
     
  5. Nov 15, 2006 #4
    SPEEDS -- always magnitudes, never directions... but magnitudes might be dependent on position (esp. radius). Think about a row in a marching band rounding a corner but trying to keep in synch -- the guys on the ouside have FAST speeds but the guys on the inside scarcely move. (The Rose Bowl parade has one camera location particularly known for shooting this shot.)

    VELOCITIES -- has the magnitude of the related speed but WITH directions.

    ANGULAR means the motion is clockwise or counterclockwise. Think of two marching band lines marching at the same rate towards a corner. As they head towards a crash collision, each two band members at the same r have the same angular speed, the guys on the outside of the corner have the fastest speeds -- and the guys on the inside have the slowest. But since one band line is rounding one way, and the other the other way, the two guys at each r have different angular velocities. Interesting enough... once they start rounding the corner, the guys collide all at the same time at the same angle... isn't that kinda cool and unexpected? (Think of joining your hands at the wrist and slapping them together slowly (or fast)).

    TANGENTIAL means tangential to the circle's arc. Think back to just one line rounding the corner, and the guy on the outside. Since he is changing direction as he moves around the radius, his tangential velocity is changing but since his motion is still in the same direction, his angular velocity is not.

    ACCELERATION relates to a change in velocity. Even if an object's speed is not varying, if its direction is then there is an acceleration. So even if the angular velocity is constant, there is an acceleration. A centripetal acceleration (pointing in) is needed to keep an object in motion at a constant radius -- it pulls the object back in. If the rate of rotation is changing, then there is both an angular and tangential acceleration.

    I found this series of interesting diagrams by googling: http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalKinematics/
    and wikipedia's section on "centripetal force" might be useful too.

    mini-edit for minor thngs
     
    Last edited: Nov 15, 2006
  6. Nov 15, 2006 #5
    Thanks a lot .... that's really helpful.
     
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