IIT JEE , AIEEE Forum - Physics , Mechanics - confusion in concept on momentum conservation

nancy_shrija

1.if a body has been rotating about its axis and we place this body on a rough surface so that it decelerates and ultimately attains the state of pure rolling.will the angular momentum remain conserved before and after it attained the state of pure rolling?

2. Q 86, hc verma, rotational motion

3. if the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?(based on rotational mechanics)

Shivam18

1. Definitely,not !! becoz according to law of conservation of momentum , every time the rotating body comes in contact with the rough surface , an impulse acts on the surface , so torque is continuously acting and therefore according to law of conservation of angular momentum , when torque acts angular momentum is not conserved

Shivam18

3. it will effect becoz , the axis of rotation will still be equidistant from the equatorial circumference but amount amount of masswill change at the poles

remember , angular velcity depend on :

1. distribution of particle(masses) around the axis of rotation

2.position of axis

nancy_shrija

the problem is that our sir used this concept of angular momentum conservation to solve 2 of the questions of hc verma, i.e, Q81,82.i did question my sir regarding this, but he said that the method was right and he showed that the hc verma solutions also use the same method. could u plz look into these questions and tell me how would u solve them?
regarding the 2nd question, the answer is that there does occur a change.the days grow longer. as per the book i am refering.but i didnt understand the reason for this.

satishrm

its simple ..................because moment of inertia of earth increases...the water in equator is farther from axis than in the pole....understand??

Shivam18

What ur sir said is exactly right , iwould like to add something to this .

when u take circular cardboard and pass a rod through its c.m(centre of mass)

when u rotate the cardboard , will rotate smooth as ever, but if you attach some blocks at the circumference and rotate, this time the angular velocity will be different from earlier one .

Shivam18

According to law of conservation of angular momentum :

I1w1 = I2w2 = constant

Where I1 & I2 are initial and final moment of inertia
w1 & w2 are initial and final angular velocity

therefore , I w = constant

point to be noted : when masses(particles ) are close to axis of rotation , moment of inertia is less while its more when masses are away from axis of rotation . Therefore, as the melted water moves away from axis, final moment of inertia increases !!!

Now from above mentioned equation , when I increases , ?w? decreases (inverse proportion)

Also , when w(angular velocity) decreases time period ?T? increases according to below relation

w = (2 ? )÷T

Betu

let's try to solve prob 81..

let's frictional force is F

, if after time t the pure rolling starts..then
final angular velockty = wr - F.r/I.t = F/m.t ..if body is a roller I=mr^2/2

then w - 2.F/m.t=F/m.t
3F/m.t=wR
F/m.t=wr/3....F/m .t is linear velocity hence pure rolling will start when v=w.R/3

if we include friction in the system..momentum is conserved

ice melting simply changes the moment of inertia ....and hence the speed

hope it helps

nancy_shrija

thanks

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