Best wishes to you.

What was your age 2 years ago

😂😂😂 great

Me too!

I think so too...

You are correct. It is that not all of the kinetic energy of the ball is in pure translation, that slows it down. The fact that it rolls gives it another mode of storing its energy (rotational KE), that is directly linked to its speed due to being in pure roll. A frictionless slider would move like a simple pendulum on that track, but a rolling ball needs to have its rotational dynamics considered to predict its period. A solid tungsten ball inside a plastic shell, would be a way to get it much closer to translational-only mechanics, by concentrating as much of the mass as close to the axis of rotation as you can..

I also think that 🤔

@@carultch Yeah agree but there must be static friction for the ball to roll.

Thanks Vivek for your kind words

I am also reading the same book currently

My pleasure!

+TheSamuelWells Yes that is correct. No need to use the words "angular momentum". The rolling ball has rotational KE (0.5*I*omega^2) + 0.5*mv^2 (here v is the tangential speed aolng the track) . A sliding object has only KE=0.5*mv^2. Therefore the average "speed" along the track will be lower for the rolling ball than for a sliding object.

+TheSamuelWells Exactly what I thought yay :D

thus, larger the diameter of the ball slower will be avg speed on track?

So if the circular track was placed on a frictionless track then would we had got the right result ?

I also thought about it and now got the confirmation!!!!!! Yeah!!!! :)

can u explain it more please....

but T=2pi ×roit under l/g

Yup.... U r right the difference is becouse of the rotational kinetic energy of the ball

correct

Teh Yong Lip it is a very rare thing for Mr. Lewin to say "correct" well done.

No s**t -- he's obviously not mentioning that because they haven't reached that part of the course yet.

I thought the energy is wasted in the noise it's producing 🤦😂

@@parthkatke6706 Me too Parth. I thought part of the energy is wasted as sound.

thank u kindly

I do not know. My guess is 0.1

Near Earth mgh works for large distances you have no choice you MUST choose the 1/r relation. Choose the signs any way you want to AS LONG AS the gravitational potential INCREASES is LARGER fir B then for A if B is farther away from the Earth surface than A.

danm me , i was wrong!!!!!!

So the ball is taking more time because normal force is doing work on it?

Let say v=dθ/dt so we have v^2 and we want the derivative so d(v^2)/dt = (d(v^2)/dv)*dv/dt which is 2*v*dv/dt so is 2*(dθ/dt)*(d^2θ/dt^2) for the time derivative of θ^2 you will get 2*θ*(dθ/dt) I didn't understand your first question

+Shadow Yes there are. Look under 8.02x

23:00 Total energy = KE + PE 34:00 ME is mechanical energy = KE + PE If any of that is magic for you I advise you to start 8.01 with lecture 1 and work you way up from there.

GREAT!

Look for 8.03x.

It's not the amplitude. It takes at least a 22 degree amplitude of a pendulum to achieve a 1% error in the period. Hyperphysics has a large amplitude pendulum period calculator, that implements the infinite series to more terms to calculate this. It's the fact that the ball rolls, while the air track slider is in pure translation, that explains it. The kinetic energy of the ball is more than just 1/2*m*v^2. It is 1/2*m*v^2 + 1/2*I*omega^2, where omega = v/r, r is the ball's radius, and I is the moment of inertia of the ball about its central axis. Put it all together, and you end up with KE_total = 1/2*v^2 *(m + I/r^2). Apply this equation to the procedure of finding the period of oscillation from this lecture and get the following. Note that big R is the track radius: T = 2*pi*sqrt(((m + I/r^2)*R) / (m*g)) Set I = K*m*r^2, where K is the factor in front of m*r^2 in moment of inertia, and get: T = 2*pi*sqrt((1+K)*R / g) Set K=0 for the case of pure translation, and get: T = 2*pi*sqrt(R / g) Set K = 2/5 for the case of a solid uniform sphere and get: T = 2*pi*sqrt(7/5 * R/g) With the given data, we predict T=2.2 seconds, for the ball rolling, which is consistent with the experiment.

@@carultch when you asked your dad for fork on dinner.

​@@carultch that was great explanation .

Yes

Most welcome

How did you get that formula, please?

@@paulproofmath323 When you do the calculations the kinetic energy for a rolling body is not (m*v^2)/2 but you have to add to this the kinetic energy from the rotation which is (I*w^2)/2 so the kinetic energy is KE= (m*v^2)/2+(I*w^2)/2 and this will give the difference

It has to do with the fact that the ball is not in pure translation, but is also rolling. There is more to its kinetic energy than just 1/2*m*v^^2.

explanation incomplete. Be more precise.

what is your age?

I am 38 years from day I born until now,but I am about 4 to 5 years in physics . I have BSC IN PHYSICS AND MATHEMATICS,but in our country's it means nothing.I have story if you dont mind (sortod1978@yahoo.com)

Khandker Tiash Azad the reaction time stays the same, but the error goes down. This is because the first error is the error on 1 oscillation, caused by the pressing of the button at the beginning of the single oscillation and at the end of the same single oscillation. In the case of 3 oscillations the button is pressed at the beginning of the first and at the end of the third, so there is no error at the end of the first, start of the second, end of the second and start of the third.

+Ayan Gangopadhyay I suggest you Google "metastable equilibrium" and also "saddle points".

sure, try it

You press the chalk in an angle about 120⁰ to the movement you do. This way friction always tries to counter the movement, and lifts the chalk.

Still in lock down

in its position

:)

@@lecturesbywalterlewin.they9259 You *did* point at the exponent of R when calculating the derivative, not at the exponent of theta... that may have triggered the student's reaction.

watch my lecture on rockets

@@lecturesbywalterlewin.they9259 thanks a lot, you truly are a lifesaver

SHM, when x=0 the force is zero. F=-kx.

I watched from 8:30 - 8:50. I cannot add to the clarity. Maybe you should watch it again.

good question. Do this problem kzfaq.info/get/bejne/et-GqZqI392sZnU.html

In one of my Bi-weekly Physics Problems I do this propblem - try to find it

kzfaq.info?o=U&video_id=MZ5eKUlO2fU

Bidisha Chakraborty No this is not correct. What is the difference between a swinging pendulum and this rolling ball?

YES! during the trip back and force, PE is being used for translation and rotation. Thus the ave speed along the track is slowed down by the rotational KE. But at the extremes when the ball stands still it should be back at the same height above the track (assuming insignificant friction and air drag).

Soumil Sahu u r wrong

@@lecturesbywalterlewin.they9259 You are right

​@@lecturesbywalterlewin.they9259😮😮

:)

you decide

Lectures by Walter Lewin. They will make you ♥ Physics. Yes sir.I got your point.

Samarth, I would suggest taking notes on the lectures without pausing. Then go back and recopy those notes neatly and make sure you can fill in any details that you didn't have time to write down during the viewing. If you can't, then watch again and if that fails, check a book. Do all that note taking by hand. I know it may sound silly, but it really does help with learning. It also wouldn't hurt to find some sample problems to work out on your own. Good luck. Physics is a fascinating subject.

Ok, in Y direction is it like modulas of SHM ( I mean only in one direction ) ?

The motion of a mass at the end of a spring is simple harmonic (SH) A*sin(wt). The motion of a pendulum of length L is also SH. For small angles of alpha_max: alpha(t)=alpha_max*sin[sqrt(g/L)*t]. x(t)=L*sin{alpha_max*sin[sqrt(g/L)*t]} and y(t)=L -- L*cos{alpha_max*sin[sqrt(g/L)*t]}. x(t) is to good approximation a SHM (for small alpha_max), but y(t) is not. That is obvious even without my equations. During one complete oscillation v(x) is zero twice but v(y) is zero 4 times.

Thank you for the detailed explanation. :)

+Lectures by Walter Lewin. They will make you ♥ Physics. Does that mean y(t) is not SHM at all or SHM with a period half that of x(t) and sin() term with it if x(t) has cos()

I gave you all the ammunition to answer this now by yourself - do not be lazy

friction lowers the amplitude but would have a near negligible effect on the frequency

You are welcome

I can't suggest any as I do not know your level. I suggest you search the web!

they are already on this channel under Playlist 8.03

You are wrong, first the air drag it will be very small so it can't be it, the reason is that the sphere rotates so it has kinetic energy due to its rotation K=(I*ω^2)/2 which you have to add in the initial relation and if you do it, you will find that the T is 2,19 instead of 1,85 which is very close with the experimental one

+Daniel Melchert Daniel, your explanation is not correct. Try again.

tachyon Tachyon you should be able to figure that out yourself. Get back to me in a week.

+Vasant Barve You explanation is incorrect.

:)

Lectures by Walter Lewin. They will make you ♥ Didn't get u sir..!!

+sweety singh When I lift an object over distance h, I have to do + work +mgh because my force and my displacement are in the same direction. The gravitational force is down. Thus gravity is doing negative work as F_grav and the displacement are in opposite direction.

+Lectures by Walter Lewin. They will make you ♥ Physics. thank you sir i get the point

I listened to it a few times. What I meant is that the eq (conservation of energy) always holds regardless of the value of theta (release angle - see picture on black board). Of course, the larger theta (at release) the larger is the total energy. E_tot= PE + KE (and it is conserved) which is always true for conservative fields regardless of how large E_tot is thus in our case regardless of the value of theta. If a non-conservative force like friction is involved, then E_tot is not conserved.

Yes. Only conservative forces have an associated potential energy. There is energy transfer with non-conservative forces, but it is an irreversible process. When friction slows down an object, energy leaves the domain of mechanical energy, and becomes thermal energy. When a human force intervenes to add mechanical energy to a system, energy enters the mechanical domain from the original form of chemical energy in the person's food supply. Energy is ultimately conserved in both of these examples, even though these are not considered conservative forces. It is just that mechanical energy isn't considered to be conserved, because other forms of energy are involved. Due to the fact that the process is irreversible, we don't keep track of a corresponding potential energy to non-conservative forces. Forces of constraint, like the normal force and tension, also don't have a corresponding potential energy, because in the ideal case, these are zero work forces. The corresponding displacement is zero, for ideal forces of constraint. Ultimately, these are a form of elasticity, and will have elastic potential energy that corresponds to them, but when deformations are insignificant, the potential energy changes are also insignificant.

1. Yes! F = -- div V 2. F=qE F and E are vectors. In case of a Resistor, the electric potential decreases in the direction of the current I, thus in the direction of E

F = -grad V is the equation, rather than F= -div V. You can't take a divergence of a scalar function. You can use the del operator on a scalar function and the only operation that becomes is the gradient. The gradient is analogous to scalar multiplication, divergence is analogous to the dot product, and curl is analogous to the cross product. The del operator is a vector of differential operators that then gets applied to the following function. In pure math, we may have a vector field capital F, and a related scalar field lowercase f. When F = grad f, with no negative sign, we call f the potential function of vector field F. This term is inspired by the physics application of a potential function, being the concept of potential energy. In Physics, it becomes necessary to introduce the negative sign in the relationship between potential energy and force, so that positive work is done by the force when potential energy decreases.

A vector field is conservative, when it is the gradient of a scalar field. If no such scalar field exists, the vector field is non-conservative. You can use the curl operation to check for whether a vector field is conservative, and if it is, there is a series of integrations to do to find that field. You'll find contradictory results in the process of integration if you attempt to calculate the potential function of a non-conservative field. In the forces / potential energy application of vector calculus, the fact that a force is conservative mean it is useful to define the concept of potential energy. It means that work done by the force is independent of path, and the potential energy can be used as a shortcut for evaluating work done by the force.

search the web

+Lectures by Walter Lewin. They will make you ♥ Physics. I mean to say that is there any lectures by you on Bulk Modulus. Thanx for replying

I may mention it in this lecture. kzfaq.info/get/bejne/n8yinJeUldLZqmw.html

martin robledo Yes of course. A sliding object on a frictionless track with the radius of my demo would have a period that I "predicted". But the ball is NOT sliding, it's rolling. It has rotational KE and that will slow down the translational motion.

+Lectures by Walter Lewin. They will make you ♥ Physics. it means that friction is taking part to make the ball to rotate

the friction is doing no work - the ball is not sliding - it's pure roll.

MATH! integral of kxdx

why integral is needed in this case Thanks for ur time prof

watch my lectures in which I cover "energy and work" this in great detail.

Lectures by Walter Lewin. They will make you ♥ Physics. Alright professor thank u for ur attention

@@ismailhaggag1859 why integral needed.................simple force is changing with the position x. if force is const: , then work is area under the rectangle of side x and that const force but here the force change linearly with x and we have to cut that rectangle diagonally gives us a right angled triangle of area 0.5bh (force *x).hope you understand ...no big deal....suggest you 3blue 1brown channel ...invent calculus yourself.....

question unclear. when een apple falls from a tree, at the moment that it starts falling its speed is zero.

@@lecturesbywalterlewin.they9259 on top of a building, we can put u=0? so why an apple will fall if we put u=0 on top of a tree? how can we put energy minus? what is the meaning of minus for energy as a scalar variable?

watch my lectures I cover this in detail

the body does not store any. It's all "stored" by gravity (mgh).

sir why is it soo hot inside of earth and why lava erruptions occur and what is the reason

use google

that explanation is ncorrect

Prof Walter please give us a note since all explanations on that question are not correct.thnx

Air drag!

NO not air drag. I leave it up to you to find the solution. It is VERY basic.

is it something with (h)?

kzfaq.info/get/bejne/et-GqZqI392sZnU.html

calculate it!!!

friction in pure rolling condition is negligible.

@@lecturesbywalterlewin.they9259 so why then does the ball slow down?

*No not right.* Any method you use will lead to a SHM ONLY for small angles.

In Lect 13 I could have derived the SHM period of a *sliding* object on the circular track in less than 5 minutes by using torque=I*alpha. However, at that time I had not introduced torques yet. Thus I decided to go the route of conservation of energy. It took 10?15? minutes? but it was useful in that the students saw for the first time that SHM can always be approached that way.

Lectures by Walter Lewin. They will make you ♥ Physics Ooops, by taking the derivative you get back to degree 1 for the sinus (sin(x)=x). I apologize. Thank you very much, professor.