Question

A particle travels in a circle of radius 20 $cm$ at a speed that uniformly increases. If the speed changes form 5.0 $\frac{m}{s}$ to 6.0 $\frac{m}{s}$ in 2.0 $s$, find the angular acceleration.

• A. 2.5 $\frac{rad}{s^2}$
• B. 5 $\frac{rad}{s^2}$
• C. 7.5$\frac{rad}{s^2}$
• D. 6$\frac{rad}{s^2}$

Answer 1

The correct option is A

2.5 $\frac{rad}{s^2}$

The tangential acceleration is given by

$a_t$ = $\frac{dv}{dt}$ = $\frac{v_2-v_1}{t_2-t_1}$

= $\frac{6.0-5.0}{2.0}\frac{m}{s^2}$ = $0.5\frac{m}{s^2}$

The angular acceleration is $a$ = $\frac{a_t}{r}$

= $\frac{0.5\frac{m}{s^2}}{20cm}$ = $2.5\frac{rad}{s^2}$.