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Old Dec 17th 2015, 09:50 AM   #1
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rotation about fixed axis

in this notes , the author gave that the IG is the moment of inertia calculated about an axis which is perpendicular to the page .....

moment of inertia calculated about an axis which is perpendicular to the page here means id due to Ft(tangential force) only ? not include Fn ( normal force ) ?


So , for the sum of moment about O , it's involve only moment due to Ft only ? Not include Fn ? Why ? can you explain ?

Last edited by ling233; Dec 18th 2015 at 05:01 AM.
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Old Dec 17th 2015, 12:52 PM   #2
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The tangential force is the only force that causes the object to accelerate its rotation (alpha), so it's the only force that needs to be considered. The force Fn acts in line with the pivot, so it does not cause rotational acceleration about the pivot.
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Old Dec 17th 2015, 05:18 PM   #3
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Originally Posted by ChipB View Post
The tangential force is the only force that causes the object to accelerate its rotation (alpha), so it's the only force that needs to be considered. The force Fn acts in line with the pivot, so it does not cause rotational acceleration about the pivot.
Then what does w (omega) refer to? Not angular acceleration? Angular acceleration not equals to rotational acceleration??
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Old Dec 18th 2015, 05:34 AM   #4
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Originally Posted by ling233 View Post
Then what does w (omega) refer to? Not angular acceleration? Angular acceleration not equals to rotational acceleration??
Omega is angular velocity (which may also called rotational velocity), and is measured in radians/second. Angular acceleration (also called rotational acceleration) is usually denoted as alpha, and has units of radians/second^2.
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Old Dec 18th 2015, 06:27 AM   #5
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Originally Posted by ChipB View Post
Omega is angular velocity (which may also called rotational velocity), and is measured in radians/second. Angular acceleration (also called rotational acceleration) is usually denoted as alpha, and has units of radians/second^2.
there is also normal component of the acceleration which can cause it to rotate , right ? why shouldnt we consider it into calculating the total moment about O ?

why the normal component of force doesnt cause the rotation about O ? it hs angular accelartion given by formula r(w^2) , am i right ?

Last edited by ling233; Dec 18th 2015 at 06:32 AM.
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Old Dec 18th 2015, 03:05 PM   #6
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The combined effect of all the forces acting on the shape is (mathematically) equivalent (when working out the overall motion of the shape) to a single force acting at the center of gravity.

The shape is tethered at the pivot point, so the portion of this combined force that is acting along the line between the pivot and the center of gravity cannot move the shape (without ripping it off the pivot).
This portion of the force is the "normal" component.

However the portion of the force that is acting at right angles to the line between the pivot and the center of gravity CAN move the shape (around the pivot).
This portion of the force is the "tangential" component.

The constraint of the fixed pivot prevents the Normal force from producing a normal acceleration,
In fact the tension within the shape generated by the pull of the pivot must balance any force trying to move the center of gravity either away from or towards the pivot,
so the resultant normal force (including this tension) must be zero.

The tangential force, obviously, creates a tangential acceleration.
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