Read the previous post first

Here's another example

In this question, you need to find out the angular acceleration of the pulley.
I'll use torque=moment of inertia*angular acceleration in a differente' fashion.

Write the torque about 'P' (the center of rotation is ALWAYS denoted by the letter 'P'):
Torque=m1*g*R-m2*g*R

Now whats the moment of inertia about 'P'? The rigid body contributes M*(K^2). But how much MOI do the masses 'm1' and 'm2' contribute? m1 contributes m1*(R^2). m2 contributes m2*(R^2).

Now, we write:
m1*g*R-m2*g*R=(M*(K^2)+ m1*(R^2)+m2*(R^2))*alpha.

Now find alpha.

Lets learn something new

Here's how I use center of rotation:

In this question, you need to find out the angular acceleration of the circular body.
I'll use torque=moment of inertia*angular acceleration in a differente' fashion.

Write the torque about 'P' (the center of rotation is ALWAYS denoted by the letter 'P'):
Torque=m*g*(2R)

Now whats the moment of inertia about 'P'? The rigid body contributes M*(K^2+R^2). But how much MOI does the mass 'm' contribute? It contributes m*(2R)^2. Note that 2R is the distance of the point 'T' from 'P'. i.e. I'm assuming 'm' to be at 'T'. Why? I don't know why but this ALWAYS works.

Now, we write:
m*g*(2R)=(M*(K^2+R^2)+ m*(2R)^2)*alpha.

Now find alpha.

Remember small things

A long wire of radius ‘a’ is carrying a direct current I.

From its surface at point A, an electron of charge −e (e > 0) escapes with velocity v₀ perpendicular to this surface.

(see Figure)

Analyze the motion to check whether the electron
- escapes to x -> ꝏ, or
- approaches some x -> x₀ (find it if yes), or
- comes back, after reaching an xmax (find it if yes) .

Ignore gravity.

< Courtesy: INPhO 2011 >

How far down the rabbit hole are we?

Well, I know this is gonna be a little boring here.. but bear with me..

Coz' I can guarantee, that if you bear with me, and you allow yourself to THINK and WONDER, you're gonna be surprised at the end.

What happens, when bits of matter, say marbles, are shot at a screen through a fine slit?

How does the pattern change, if we add another slit of the same thickness?

Now let's look at waves.

What pattern (I don't wanna know what you 'call' that pattern, but what it actually is) can you see on the screen if water ripples through a single slit?

( You may assume that a stone is dropped in water in front of a slit half submerged in water. )

Again tell me, what changes, if I add a second slit.

So now, we know what happens when matter passes through 2 slits, and what happens when waves pass through 2 slits. (Don't we?)

Let's go again.

What do we expect to see if electrons (tiny tiny bits of matter) are shot at a screen through a single slit?

And what if I add a second slit??

THINK.

If you think you have the answers, click here.

As of discussing together.. well, we can do that later, but first I want you people to answer these on your own.

Let's make this simpler.. assume that the slits are thin enough, not to permit more than one particles side-by-side.
And yes, our screens are 'intelligent', they record all intensity patterns. (:

Fear Factor

A spool of radius 100m and mass 100kg has 100 grooves of radii 1m, 2m, ..., 100m. We use pulleys to suspend masses from the grooves as shown. The mass (i)kg is associated with the groove of radius (100-i)m.

Find the angular acceleration of the spool.

So you don't know how to find the Radius of curvature?

Lets try it again.

A particle is projected with a velocity 10m/s at an angle 37* with horizontal. Whats the radius of curvature at t=0? At what instant is the radius of curvature minimum?

Find the radius as a function of time.

Solution: Radius of curvature

F=1i`+2j`+3k`
V=-2i`+3j`-k`

Now, the component of force perpendicular to the velocity is (m*|V|^2)/r.

This component is |F|*Sin(Q)=2*14/r
or sqrt(14)*Sin(Q)=(2*14)/r

or r=(2*sqrt(14))/Sin(Q)

Q is the angle b/w the 2 vectors F and V.

Radius of Curvature

Do you know how we find the radius of curvature of a particle's path?

A force 1i`+2j`+3k` acts on a particle (mass=2) moving with a velocity -2i`+3j`-k`. What is the radius of curvature of the particle's path at this instant?

Angular Momentum

A particle is projected with speed 'v' at an angle 'Q' with the horizontal. Find its angular momentum about the point of projection after time 't'.

7 elastic beads for the Dwarf-lords, in their halls of stone

Seven identical beads are sliding on a meter rod as shown. Their positions and velocities are listed. A positive velocity indicates motion to the right.

When a bead slides off the meter rod, a Dragon awakes. Presently, its t=0.

At what times does a Dragon awake? Note that a total of 7 Dragons will wake up. List all the 7 time instants.

Click the image to enlarge and notice the minus signs.