A horizontal solid disc is set into rotation about its central axis

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

Problem

A horizontal solid disc is set into rotation about its central axis. It starts from rest and attains a constant angular acceleration of

4\,\text{rad}\,\text{s}^{-2}

. A small particle

P

is fixed on the disc at a distance

0.20\,\text{m}

from the axis. (i) Derive an expression for the magnitude of the linear (resultant) acceleration of

P

as a function of time

t

after the motion begins. (ii) Show that the acceleration of

P

makes an angle of

45^{\circ}

with the radial line at a certain instant, and determine the time

t_{1}

at which this occurs. (iii) Calculate the numerical value of the resultant linear acceleration of

P

and its angle with the radial line at the time

t_{1}

obtained in part (ii).