Angular acceleration x radius= Acceleration of center of mass ?

AI Thread Summary
The discussion centers on the relationship between angular acceleration and linear acceleration in rotating bodies. It clarifies that angular acceleration multiplied by radius gives the tangential acceleration of a point on the body, not the acceleration of the center of mass. The correct formula is atan = αr, where atan is the tangential acceleration, α is angular acceleration, and r is the distance from the axis of rotation. The relationship acm = αr applies only when a body is both rotating and translating, such as a sphere rolling without slipping. Misunderstandings arise regarding the definitions and contexts of these terms, particularly the distinction between center of mass and center of rotation.
AakashPandita
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For a rotating body,
(angular acceleration x radius)= Acceleration of center of mass ?

But a rotating body can have angular acc. even if it is not translating. what is wrong?
 
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no no no... angular acc. x radius = the linear acc. of a point on the body , ie the tangential velociti of that point with respect to the centre of mass
 
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the point is moving around the body with a speed= R x α
where α= angular acceleration
 
Hi Aakash...

The correct relationship for a point on a rotating body is

atan = αr where ,

atan=tangential acceleration of the point with respect to center of the axis

α = angular acceleration of the rotating body

r= distance between the point and the center of the axis

AakashPandita said:
For a rotating body,
(angular acceleration x radius)= Acceleration of center of mass ?

But a rotating body can have angular acc. even if it is not translating. what is wrong?

The relationship acm = αr is a constraint which is sometimes obtained in cases when a body is rotating as well as translating.

For eg. a sphere rolling without slipping on floor .
 
Tanya Sharma said:
Hi Aakash...

The correct relationship for a point on a rotating body is

atan = αr where ,

atan=tangential acceleration of the point with respect to center of the axis

α = angular acceleration of the rotating body

r= distance between the point and the center of the axis



The relationship acm = αr is a constraint which is sometimes obtained in cases when a body is rotating as well as translating.

For eg. a sphere rolling without slipping on floor .

i have told the same...:cool:
 
Kishlay said:
i have told the same...:cool:

Your language is sloppy and inaccurate .

Kishlay said:
no no no... angular acc. x radius = the linear acc. of a point on the body , ie the tangential velociti of that point with respect to the centre of mass

The item in red should be acceleration.

Again ,instead of center of mass,you should have used center of rotation.

Kishlay said:
the point is moving around the body with a speed= R x α
where α= angular acceleration

That doesn't make any sense . Neither the point is moving around the body ,nor is speed equal to R x α
 
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thanks.
 

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