prove centripetal force = m(v^2/r)

Question

mathslover · Answer

$$\huge{m\frac{v^2}{r}}$$

mathslover · Answer

@UnkleRhaukus

mathslover · Answer

@waterineyes

mathslover · Answer

@Vaidehi09

anonymous · Answer

where is our starting point?

anonymous · Answer

i think we can start with v = rw?

mathslover · Answer

did u mean w--> omega ?

anonymous · Answer

yes

mathslover · Answer

K ! so f = ma 
a = v-u/t = rw-u/t

anonymous · Answer

If an object is undergoing uniform circular motion then

$$R= r \cos \omega t \ i+ r \sin \omega t \ j\ V=\frac{dR}{dt} = -r \omega \sin \omega t \ i+ r \omega \cos \omega t \ j \ a=\frac{dV}{dt}=  -r \omega^2 \cos \omega t \ i- r \omega^2 \sin \omega t \ j\ \left| a \right|=r \omega^2$$

anonymous · Answer

then F=mrw^2
        v=rw
        w=v/r
                       ----->  F=m v^2/r

anonymous · Answer

sorry, i lost my net there for a while. and @mathslover, don't proceed that way. @mukushla 's derivation is the right way.

mathslover · Answer

ok thanks a lot @mukushla and @Vaidehi09

anonymous · Answer

if u want @mathslover may i also contribute some

anonymous · Answer

When an object is in circular motion, it need centripetal force.
A red ball is attached to a green cord (neglect its mass)
passing through a small hole in a friction less, horizontal table.
The red ball is initially orbiting in a circle of radius r with velocity v. 
A black ball is tied to the other end of the green cord.
If it is in equilibrium,

the gravitational force of the black ball Fg = Mg , 
provides the centripetal force Fc needed.
$$Fc = m v^2/r = m w^2 r ( v=w*r )$$

$$Fg = Fc     $$
 then i.e.
$$ Mg = m w^2 r $$

mathslover · Answer

thanks a lot to u too

rishabh.mission · Answer

Centripetal Acceleration, ac = v2/r  
ac = centripetal acceleration (m/s2)
Centripetal Force According Newton's second law the centripetal force can be expressed as

Fc = m ac

    = m v2/r         (2)

where

Fc = centripetal force (N)

m = mass (kg).

anonymous · Answer

$$F=mac$$
where ac is centripetal acceleration therefor
$$ac=v ^{2}/r$$
$$F=mv^2/r$$

mathslover · Answer

thanks a lot @muhammad9t5and @rishabh.mission

mathslover · Answer

@muhammad9t5

anonymous · Answer

@mathslover friend then click on best answer to give me medal if you like. Thanks.

mathslover · Answer

I am  also confused to give medal to whom !!!.. sorry