Question

Show how to obtain equation (4) from equations (1), (2), and (3). Please show each step.

(1) Tr=Iα
(2)α=a/r
(3) mg-T-f=ma

(4) I=mr²[(g/a)-1-(f/ma)]

Answer 1

we have an equation,   T r = I                                                    { eq.1 }

and    = a / r

inserting the value of '' in above eq.

T r = I (a / r)

or    I = T r² / a                                                                                   { eq.2 }

We have anothere equation given as :

m g - T - f = ma                                                                                { eq.3 }

T = mg - ma - f

or T = m (g - a) - f                                                                         { eq.4 }

inserting the value of 'T' in eq.2, we get

I = [m (g - a) - f] r² / a

I = m r² [(g / a) - 1 - (f / ma)]

Hence proved.