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

`\alpha=504.0357(rad)/(s^2)`

Step-by-step explanation:

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

`\alpha=(\Delta \omega)/(\Delta t) =(\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(rev)/(min) *(2\pi rad)/(1rev) *(1 min)/(60s)  =1168\pi (rad)/(s)`

Finally, replacing the data in the angular acceleration equation:

`\alpha=(1168\pi -0)/(7.28-0) =(1168\pi)/(7.28)=504.0357444\approx504.0357 (rad)/(s)`