A disc rotates about its axis with a constant angular acceleratio… - Vidyadip

Question

A disc rotates about its axis with a constant angular acceleration of $4\ \text{rad/s}^2.$ 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.

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Answer

$\text{t}=1\text{ sec},\ \text{r}=1\text{ cm}=0.01\text{m}$
$\alpha=4\text{ rad/s}^2$
Therefore $\omega=\alpha\text{t}=4\text{ rad/s}$
Therefore radial acceleration,
$\text{A}_{\text{n}}=\omega^2\text{r}=0.16\text{ m/s}^2=16\text{ cm/s}^2$
Therefore tangential acceleration,
$\text{a}_{\text{r}}=0.04\text{ m/s}^2=4\text{ cm/s}^2.$

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