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.

Evaluate: (i) omega (ii) omega^(2) (iii) omega^(3)

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

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

In the relation ( dy)/( dt) = 2 omega sin ( omega t + phi_(0)) , the dimensional formula for omega t + phi_(0) is

The differentia equation obtained on eliminating A and B from y=A cos omega t+b sin omega t, is y^(+)y'=0 b.y^(-omega)-2y=0 c.y^(=)omega^(2)y d.y^(+)y=0

the angular velocity omega of a particle varies with time t as omega = 5t^2 + 25 rad/s . the angular acceleration of the particle at t=1 s is

Let omega_1 and omega_2 be the roots of omega^2+aomega+b=0 . If origin, omega_1 and omega_2 form an equilateral triangle then

If i_(1) = 3 sin omega t and i_(2) =6 cos omega t , then i_(3) is

Find the dimensions of a. angular speed omega angular acceleration alpha torque tau and d. moment of interia I. . Some of the equations involving these quantities are omega=(theta_2-theta_1)/(t_2-t_1), alpha = (omega_2-omega_1)/(t_2-t_1), tau= F.r and I=mr^2 The symbols have standard meanings.