In motion with no slipping, Textbook said Fp should be smaller or equal than sta

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In motion with no slipping, Textbook said Fp should be smaller or equal than static friction.I dont know why. In my view,No slipping motion requires velocity of contact be zero. So Fp=mgsin(thera) should be equal But this is not used Why did i think wrong? 8.6 Examples of The Laminar Motion of a Rigid Body 349 Motion with No Slipping tact is veryroughethat no slippingcanoccur,that is, if(Psu,Fy atic friction, we have the following relations where is cofict of st the Xcm = a = @ (8.6.8a) (8.6.8b) ere is the angle of rotation. Equation 8.6.7 can then be written (8.6.9) Substituting this value for Fr into Equation 8.6.3 yields (8.6.10) Solving for , we find g sin where om is the radius of gyration about the center of mass: The body, teiore, rolls omstant imear acceleration and with constant angular acceleration down the phare withe by virtue of Equations 8.6.8a and b. For example, the acceleration of a uniform cylinder a is g sin 1 +(1)-38 sin = 2a2/5) is (8.6.12 whereas that of a uniform sphere ( sin (8.6.1

Explanation / Answer

Textbook said Fp should be smaller or equal than static friction.I dont know why.

because if Fp is larger than limiting value of static friction then rolling body cannot provide enough friction to avoid skidding or slipping. if Fp is larger then body will not roll, instead it will slip/skid. same happens when we apply sudden break to fast moving car. tyre of car skids as road cannot provide that much friction

In my view,No slipping motion requires velocity of contact be zero.

yes, this condition is true. but i feel you are mixing velocity with acceleration thats why getting confused. at point of contact, velocity is zero but there is net force. so that point is accelerating actually but only thing is, that point is passing through zero velocity. means from some negative value like -0.1 m/s to +0.1m/s .

So Fp=mgsin(thera) should be equal

if these are equal then net force is zero. then body does not have translational motion and body will rotate at same point as both forces are not acting along same line. same happens in pulley rotating.

in rolling, body rotates also as well it moves from one point to another point. so net force must not be zero.

so we cannot use this relation and this condition applies when body is in equilibrium.

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