Awheel is rotating about an axis that is in the z-direction. the angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 16.0 s . we have taken counterclockwise rotation to be positive.
(a) is the angular acceleration during this time interval positive or negative?
(b) during what time interval is the speed of the wheel increasing? decreasing?
(c) what is the angular displacement ofthe wheel at t = 7.00s?

Explanation:

Hello, I will answer each numeral question by numeral.

a)

taking into account that the wheel speed increases linearly with time, and that the direction of rotation is hourly we can conclude that the acceleration has the same direction as the speed, so the acceleration is negative

b)the wheel speed increases in a time interval of 16s, remember that time does not decrease and is always positive, it is impossible that there is a negative time because it has no direction

c)

to find the displaced angle we use the kinematic equations that define the displacement of a rotating body

first we find the acceleration

where

Vf = final speed

=-6-4=-10rad/S

Vo = Initial speed

=-6rad/s

t=16s

a=acceleration

solving

finally we find the displacement

α=VoT+0.5at^{2}    

the angular displacement ofthe wheel at t = 7.00s is    -66.5Rad