Question

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

• A. $16\frac{cm}{s^2},4\frac{cm}{s^2}$
• B. $0.16\frac{cm}{s^2},0.04\frac{cm}{s^2}$
• C. $16\frac{m}{s^2},4\frac{m}{s^2}$
• D. $1.6\frac{cm}{s^2},0.4\frac{cm}{s^2}$

Answer 1

The correct option is A

$16\frac{cm}{s^2},4\frac{cm}{s^2}$

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

$a$ = 4 $\frac{rd}{s^2}$

Therefore $\omega$ = $at$ = 4 $\frac{rad}{s}$

Therefore radial acceleration,

$A_n$ = ${\omega }^{2}r$ = 0.16 $\frac{m}{s^2}$ = 16 $\frac{cm}{s^2}$

Therefore tangential acceleration, $a_r$ = $ar$ = 0.04 $\frac{m}{s^2}$ = 4 $\frac{cm}{s^2}$.