Question:
A disc rotates about its axis with a constant angular acceleration of $4 \mathrm{rad} /{ }^{S^{2}}$. Find the radial and tangential accelerations of a particular at a distance of $1 \mathrm{~cm}$ from the axis end of the first second after the disc starts rotating.
Solution:
$\omega_{0}=0, \alpha=4 \mathrm{rad} /{ }^{s^{2}} ; \mathrm{t}=1 \mathrm{sec}$
$\omega={ }^{\omega} 0_{+} \alpha_{t}$
$\omega=4 \mathrm{rad} / \mathrm{sec}$
Radial acceleration $=\mathrm{R}^{\omega^{2}}$
$=(0.01)^{(4)^{2}}$
$=0.16^{\mathrm{m} / \mathrm{s}^{2}}$
$=16^{\mathrm{cm} / \mathrm{s}^{2}}$
Tangential acceleration
$a_{T}=r a$
$=(0.01)(4)$
$=0.04 \mathrm{~m} / \mathrm{s}^{2}$
$=4 \mathrm{~cm} / \mathrm{s}^{2}$