Help with deriving an Equation from 4 others

[blaZkowicZ]

Homework Statement

Our teacher assigned us this problem of trying to derive and equation from 4 simpler equations and I just can't seem to get the correct answer so I need some help.

a= M₁g / (1/2)M₂+M₁

a= acceleration
M₁= Mass 1
M₂= Mass 2
g= gravity
R= radius
T= tension
I= moment of inertia
\alpha= angular acceleration

Homework Equations

These are the four equations at which I am supposed to derive the equation above from

a) RT = I\alpha
b)M₁g-T = M₁a
c)a = \alphaR
d) I = (1/2)M₂R²

The Attempt at a Solution

I am very close to the answer but no cigar

a=\alphaR

a= (RT/I)*R

a= [ RTR / (1/2)M₂R²]

a= T / (1/2)M₂

a= -(M₁a) + M₁g / (1/2) M₂a= (M₁g) / ((1/2)M₂ + M₁a

As you can see I can get all of it correct except for the "a" on the bottom of the equation is wrong. Does anyone have any idea on what to do here? Thanks in advance.

 

[semc]

How did you get the last step? if you want 'a' just group them together.

 

[Redbelly98]

Homework Statement

Our teacher assigned us this problem of trying to derive and equation from 4 simpler equations and I just can't seem to get the correct answer so I need some help.

a= M₁g / (1/2)M₂+M₁

a= acceleration
M₁= Mass 1
M₂= Mass 2
g= gravity
R= radius
T= tension
I= moment of inertia
\alpha= angular acceleration

Homework Equations

These are the four equations at which I am supposed to derive the equation above from

a) RT = I\alpha
b)M₁g-T = M₁a
c)a = \alphaR
d) I = (1/2)M₂R²

The Attempt at a Solution

I am very close to the answer but no cigar

a=\alphaR

a= (RT/I)*R

a= [ RTR / (1/2)M₂R²]

a= T / (1/2)M₂

a= -(M₁a) + M₁g / (1/2) M₂

It looks good up to here, but you really should use parentheses to group the terms properly:

a= -(M₁a + M₁g) / ((1/2) M₂)

I suggest multiplying on both sides by (1/2)M₂, so that you won't have a complicated fraction to deal with. Then it will be easier to use semc's suggestion of grouping the a's together.