Question

A disc rotates about its axis with a constant angular acceleration of 4 rad/s${}^2$. Find the radial and tangential accelerations of a particle at a distance of 1 cm from the axis at the end of the first second after the disc starts rotating.

Answer 1

t = 1 sec, r = 1 cm = 0.01 m

$\alpha$ = 4 rad/s ${}^2$

Therefore $\omega$ = $\alpha$t = 4 rad/s

Therefore radial acceleration,

$a_n$ = ${\omega }^{2}r$=(4${}^2$ $\times$ 0.01)

= 0.16 m/s ${}^2$=16~m/s ${}^2$

Therefore tangential acceleration,

$a_T$ = $\alpha r$ = 0.04$m/s^2$

=4 cm/s${}^2$