Rotation of a solid body about CM?

[gursimran]

We know when a body is given a impulsive force in total vaccum, it rotates along with translation about the centre of mass. Now the question is why does it rotate only about the CM and not any other axis. We al know this seems obvious due to insinct but how can the theory explain it. Does any other effects like air drag effect this?

PS -consider the cases when the body does not rotate about its CM and put emphasis on geometric centre.. why does the not rotate naturally about geometric centre..

 

[tiny-tim]

welcome to pf!

hi gursimran! welcome to pf!

it's good ol' Newton's first law …

(ok, strictly that's only for point masses, but we can extend it to rigid bodies using Newton's third law to cancel out all the internal forces! )

if the only force is impulsive, that means that after the impulse time, there are no forces acting on it

if there are no forces acting on it, then its centre of mass must move with constant speed in a straight line

if it was rotating about some other point in the body, that would have to be moving in a straight line …

they can't both be moving in a straight line unless there's no rotation

 

[gursimran]

hi gursimran! welcome to pf!

it's good ol' Newton's first law …

(ok, strictly that's only for point masses, but we can extend it to rigid bodies using Newton's third law to cancel out all the internal forces! )

if the only force is impulsive, that means that after the impulse time, there are no forces acting on it

if there are no forces acting on it, then its centre of mass must move with constant speed in a straight line

if it was rotating about some other point in the body, that would have to be moving in a straight line …

they can't both be moving in a straight line unless there's no rotation

Thanks tiny-tim for reply, I got it. I just seem to forget the fundamentals..
1.Does it means that a body can rotate about a point other than CM in air (due to drag)

2.Ok then how do you relate this to that a body has minimum centre of interia about the CM..

3. Another thing that comes is that its not possible for a body to rotate about a point other that CM if only internal forces act inside the body..

 

[tiny-tim]

hi gursimran!

(just got up :zzz: …)

1.Does it means that a body can rotate about a point other than CM in air (due to drag)

yes

2.Ok then how do you relate this to that a body has minimum centre of interia about the CM..

(you mean moment of inertia )

sorry, not following you

3. Another thing that comes is that its not possible for a body to rotate about a point other that CM if only internal forces act inside the body..

yes, because with no external forces, the centre of mass must move in a straight line

 

[gursimran]

hi gursimran!

(just got up :zzz: …)


yes


(you mean moment of inertia )

sorry, not following you

I mean we can explain the other way around in a bit non technical fashion like this. The moment of intertia is least about the CM of a body and so it rotates with minimum effort. So the body rotates about the axis where the effort is minimum. I know its very non technical but...

 

[tiny-tim]

The moment of intertia is least about the CM of a body and so it rotates with minimum effort. So the body rotates about the axis where the effort is minimum.

no

the moment of inertia is in an equation relating torque to angular velocity

but the angular velocity is the same about any point

"effort" has nothing to do with it

 

[gursimran]

ok then thankyou very much ... i think i got most of the stuff :)