A sanding disk with rotational inertia 1.2 x 10⁻³ kg. m² is attached to an electric drill whose motor delivers a torque of 16 N. m. Find (a) The angular momentum and (b) the angular speed of the disk 33 ms after the motor.

The angular momentum of the sanding disk is 0.528 kg.m^2.s^-1 and its angular speed is 440 s^-1

Explanation:

Given:

Torque ( ) delivers by the electric motor =

Time taken = 33 ms (milliseconds) =

Moment of Inertia,MOI ( ) =

We have to find the angular momentum () and angular speed ().

Notes:

Angular momentum in terms of torque and time ,

And

Angular momentum in terms of MOI and speed,

So,

a) Angular momentum.

⇒

⇒

⇒

The angular momentum of the sanding disk is 0.528 kg.m^2.s^-1

b)Angular speed.

⇒  

⇒

Plugging the values of and MOI

⇒

⇒

The angular speed of the disk is 440 s^-1

So the angular momentum of the disk is and the angular speed is .

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

gas and liquid