A disc rotates about its axis with a constant angular acceleration of 4 $r a d / s^{2}$ . 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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Solution

Given:
The angular acceleration of the disc is $α = 4 r a d / s e c$
The radius of the circular path $r = 1 c m$

We know that the tangential acceleration is given as:
$a_{t} = r α$
$a_{t} = (0.01) \times 4$
$a_{t} = 0.04 m / s^{2} = 4 c m / s^{2}$

Then, using law of motion equation to find velocity
$v_{t} = 0 + a_{t} (t)$
$v_{t} = (0.04) \times 1 = 0.04 m / s$

Also, we can find
$a_{r} = \frac{v^{2}}{r} = \frac{(0.04)^{2}}{0.01} = 0.16 m / s^{2} = 16 c m / s^{2}$

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