" 2.Show that "(a). omega=omega_(0)+alpha t

Obtain the equation omega = omega_(0) alpha t from first principles.

Derive the three equation of rotational motion (i) omega = omega_(0) + at (ii) theta = omega_(0)t + 1/2alpha t^(2) (iii) omega^(2) = omega_(0)^(2) + 2alpha theta Under constant angular acceleration. Here symbols have usual meaning.

Drive the equations of rotatory motion, omega^2 - omega_0^2 = 2 alpha theta and theta= omega_0^t + 1/2 alpha t^2 , where every letter has its usual meaning.

If omega is a complex cube root of unity, show that (a+b) + (a omega +b omega^2 )+(a omega^2 +b omega ) =0

If alpha, beta are the roots of x^(2) + px + q = 0, and omega is a cube root of unity, then value of (omega alpha + omega^(2) beta) (omega^(2) alpha + omega beta) is

If omega is a complex cube root of unity.Show that Det[[1,omega,omega^(2)omega,omega^(2),1omega^(2),1,omega]]=0

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4 .

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4

Show that det ([1,omega,omega^(2)omega,omega^(2),1omega,omega^(2),1omega^(2),1,omega])=0 where omega is the non-real cube root of unity =0 where omega is