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

Given:

The angular acceleration of the disc is $\alpha =4rad/sec$

The radius of the circular path $r=1cm$

We know that the tangential acceleration is given as:

$a_t=r\alpha$

$a_t=\left(0.01\right)\times 4$

$a_t=0.04m/s^2=4cm/s^2$

Then, using law of motion equation to find velocity

$v_t=0+a_t\left(t\right)$

$v_t=\left(0.04\right)\times 1=0.04m/s$

Also, we can find

$a_r=\frac{v^2}{r}=\frac{(0.04{)}^2}{0.01}=0.16m/s^2=16cm/s^2$