The h Bar

4:00 PM

or actually, the physical situation might change as a whole (because we don't have a perfectly flat sheet), so never mind I guess

Manolis Lyviakis

cant understand how did he find that 88=u

i get why max velo is 120mph

and i get why he uses only rotational accelaration formula

but how did he found the angular velocity in order to find u

Sha Vuklia

I retract my last conclusion; we can still argue that the field points in the same direction, because if we just get extremely close to the surface, then the biggest contribution will be due to our small (flat) patch itself, so we are really dealing with a symmetrical situation if we flip everything @PrathyushPoduval I don't know if you agree, but for me it all sounds solid now! So I'm satisfied

John Rennie

4:16 PM

@ManolisLyviakis it's simply the equation for centripetal acceleration in circular motion:

$$ a = \frac{v^2}{r} $$

where $v$ is the velocity of the outsdie of the wheel and $r$ is the radius of the wheel.

Manolis Lyviakis

ye i get that

the number 88 where it came from

u=88

u=angular velo * Radius

radius=2feet

i dont get how he found angular velocity? i know the truck moves in 60mph so 1 mile min so 1/60 miles per sec

and the circum of the wheel is 4π feet

John Rennie

60 mph is 88 feet per second

Manolis Lyviakis

so i was on the right track

John Rennie

In the rest frame of the truck the outside of the tyre is moving at 60 mph/88 fps

Manolis Lyviakis

ohh so in rotational accelaration

i use the translational speed?

John Rennie

4:25 PM

You use the tangential speed at the distance $r$

Or you can write $a = \omega^2 r$ if you prefer to use angular velocity. Since $v = r \omega$ the two equations are the same.

How come you are doing questions where you have to calculate things in feet per second? You're in Greece aren't you?

Manolis Lyviakis

how do i find the tangential speed im given only the tanslational speed

yes im in greece

its just the book i follow xD

John Rennie

@ManolisLyviakis suppose you're in the rest frame of the truck so the centre of the wheel is stationary. now the ground is flashing past you at 60 mph. Yes?

Manolis Lyviakis

yeap

John Rennie

And the edge of the tyre is in contact with the ground, and it isn't skidding, so the tangential velocity at the edge of the tyre must also be 60 mph - the same as the speed of the ground.

Manolis Lyviakis

hm..

not zero?

John Rennie

4:32 PM

3 mins ago, by John Rennie

@ManolisLyviakis suppose you're in the rest frame of the truck so the centre of the wheel is stationary. now the ground is flashing past you at 60 mph. Yes?

Manolis Lyviakis

yea i understand it had to do with the frame of refenrencce

so im on the track

John Rennie

So in the rest frame of the truck the tangential velocity of the tyre is 60 mph

Manolis Lyviakis

i see the ground moving

truck*

and the wheel rotating

and the point where is contact

it must seem to me

like stationari

stationary ?

so they have the same veloc?

thannks ill give it some time of thinking

@JohnRennie so he ddnt calculate ω ? just to be clear .

John Rennie

No, the solution doesn't involve calculating the angular velocity

Manolis Lyviakis

and how do i know the tang velo is constant ( i know im asking stupid questions).

cause f the wheel was accelrating so would the truck

:P

John Rennie

4:47 PM

The wheel and truck aren't accelerating

Any object moving in a circle about a central axis has a centripetal acceleration.

Centripetal force

A centripetal force (from Latin centrum, "center" and petere, "to seek") is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along...

Manolis Lyviakis

tangential velocity isnt the rotational velocity?

Emilio Pisanty

@Semiclassical you around?

the Riemann surface for graphene is killing me

I tried doing just a single Dirac cone and it's still killing me

but on the other hand

Manolis Lyviakis

the velocity of a point in the wheel in its circumf. is not constant. is the translational velocity+the rotational velocity and depends on the angle between them . Now we consider that we move with the track. So we dont care about the translational part.So when asked about the magnitude acceleration is it on a specific point? ??

Emilio Pisanty