Question

A dentist’s drill starts from rest. After 7.28 s of constant angular acceleration it turns at a rate of 35040 rev/min. Find the drill’s angular acceleration. Answer in units of rad/s 2 .

Answer 1

Answer:

$\alpha=504.0357\frac{rad}{s^2}$

Explanation:

Angular acceleration is defined as the change experienced by angular velocity per unit of time. Mathematically can be expressed as:

$\alpha=\frac{\Delta \omega}{\Delta t} =\frac{\omega_f-\omega_o}{t_f-t_i}$

From the rest:

$\omega_o=0\\t_0=0$

Now, before calculating the angular acceleration, let's convert rev/min to rad/s

$35040\frac{rev}{min} *\frac{2\pi rad}{1rev} *\frac{1 min}{60s}  =1168\pi \frac{rad}{s}$

Finally, replacing the data in the angular acceleration equation:

$\alpha=\frac{1168\pi -0}{7.28-0} =\frac{1168\pi}{7.28}=504.0357444\approx504.0357 \frac{rad}{s}$