"a grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. the angular speed is then increased to 12 rad/s over the next 4.0 seconds. assume that the angular acceleration is constant. what is the average angular speed of the grindstone? "

The average angular speed of the grindstone is 10 rad/s

Let's recall Angular Speed formula as follows:

where :

ω = final angular speed ( rad/s )

ω₀ = initial angular speed ( rad/s )

α = angular acceleration ( rad/s² )

t = elapsed time ( s )

θ = angular displacement ( rad )

Given:

radius of the grindstone = R = 4.0 m

initial angular speed = ω₀ = 8.0 rad/s

final angular speed = ω = 12 rad/s

elapsed time = t = 4.0 seconds

Asked:

average angular speed = ?

Solution:

Firstly , we will calculate angular displacement as follows:

Next , we could calculate the average angular speed as follows:

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics

the independent variable, or the one that is intentionally manipulated is the speed.

6 cos 34, 6 sin 34 trig