Initially, a ball has an angular velocity of5 rad/s counterclockwise. some time later, after rotating through a total angle of 5.5 radians, the ball has an angular velocity of 1.5 rad/s clockwise. (a) what is the angular acceleration? (b) what is the average angular velocity? (c) how much time did it take to change the speed

a) 2.1 rad/s² clockwise

b) 1.8 rad/s counterclockwise

c) 3.1 s

Explanation:

Take counterclockwise to be positive.

Given:

ω₀ = 5.0 rad/s

ω = -1.5 rad/s

Δθ = 5.5 rad

a) Find α

ω² = ω₀² + 2αΔθ

(-1.5 rad/s)² = (5.0 rad/s)² + 2α (5.5 rad)

α = -2.1 rad/s²

b) Find ω_avg

ω_avg = ½ (ω + ω₀)

ω_avg = ½ (-1.5 rad/s + 5.0 rad/s)

ω_avg = 1.8 rad/s

c) Find t

Δθ = ½ (ω + ω₀) t

(5.5 rad) = ½ (-1.5 rad/s + 5.0 rad/s) t

t = 3.1 s

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force