For a rotating platform

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

Problem

For a rotating platform, the angular acceleration is maintained in three successive intervals as follows:

\alpha = \alpha_{1}

for

0 \le t < t_{1}

\alpha = \alpha_{2}

for

t_{1} \le t < t_{2}

\alpha = \alpha_{3}

for

t_{2} \le t \le t_{3}

, where

\alpha_{1},\,\alpha_{2},\,\alpha_{3}

are non-zero constants (their signs may differ). The platform is at rest at

t = 0

. (i) Derive an expression for

\omega(t)

valid for each interval, ensuring continuity at

t_{1}

and

t_{2}

. (ii) Hence obtain expressions for the angular displacement

\theta(t)

in each interval with

\theta(0)=0

. (iii) Show algebraically that the total change in angular velocity over

0

t_{3}

equals the area under the piecewise

\alpha

–

t

graph in the same interval.