A rotor undergoes a two-stage rotation about a fixed axis

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A rotor undergoes a two-stage rotation about a fixed axis. Starting from rest it is provided a uniform angular acceleration

\alpha_{1}=6\,\text{rad\,s}^{-2}

for a time

t_{1}

, after which a uniform angular deceleration

\alpha_{2}=-2\,\text{rad\,s}^{-2}

is applied for a further time

t_{2}

, bringing the rotor to rest once more. During the entire motion the rotor turns through a net angle of

150\,\text{rad}

. (i) Using only the given data, derive two independent equations relating

t_{1}

and

t_{2}

. (ii) Solve these equations to find the numerical values of

t_{1}

and

t_{2}

. (iii) Determine the maximum angular speed attained by the rotor during the motion.