Doubt from Rigid Body Dynamics

@Gaurav_Singh

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Just one question why we have converted Omega here in rad/s we can also apply formula in rev/s

no reason i always just convert it for getting all in standard terms

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I am not conceptually clear here need help

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Is it D?

Assume that sphere is moving towards right with a speed v and angular velocity \omega (rotating in clock-wise direction).
After collision, v is towards left. The point in contact with the ground is not at rest now (its speed is v+r\omega). So, it will be slipping until the sphere acquires rolling without slipping, which will happen only after some time.
So D is the correct answer.

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Why is it necessary that the sphere will have angular velocity omega a long time after the collision? @Cooljet123

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Friction continues to act until no slipping condition is achieved (I meant any general omega, not the initial one)…let me change it. Thanks for pointing out.

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Is there any condition to apply
Torque = I × alpha
Means when we can’t apply it

torque =I * alpha is applicable only about COM or abt points which r at rest if u want to apply from a moving point then we need to consider pseudo force passing throught COM also

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Can u send such a question where we need to make use of pseudo torque? (If u have such a question). Yeah like a question where we are forced to calculate pseudo torque

Do you mean where pseudo force produces a Torque? Or something else?

Bro always apply torque at COM that makes the torque of pseudo force zero so it’s quite helpful to us.
Well that means it do not have a condition right ?

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no it has conditions
the torque equation tou=Ialpha is used only abt a point which belongs to the body only if it doesnt belong to the body then u cant apply that equation
i ll give an example
case 1:let us assume that a rod is rotating abt an axis passing through COM on a horizontal plane now if u want to apply torque abt an end point of rod then u ll write pseudo force torque and torque due to axis
case 2: try doing same abt a point on the ground just below the point u considerd above as there is no pseudo force (its belonging to ground hece it ll not move) now torque is only due to axis of rotation hence u ll get different angular acclerations
but do u think u ll observe 2 different acclerations in both casses ans is no
in second case u cannot apply that equation u need to differentate angular momentum
L=m r×vcom+icom
omega
differentaite above one u ll get same angular accleration as in case 1


My 3 equations : linear momentum conservation , Angular momentum conservation , coefficient of restitution but still not getting the answer .

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Is it single correct ?
I’m getting W = V/L
omega about the rod’s centre
Didn’t check that energy terms…what did you get

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What’s the answer ?
I m getting W=v/l and option d.

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And is A and C

Sure ?
Bcoz even on websites like Toppr and Doubtnut , they hve got W=v/l for exact same question

Yeah , ans in D C Pandey is A and C .
@AshWin please try this question