A motorcycle, which has an initial linear speed of 5.0 m/s, decelerates to a speed of 3.5 m/s in 4.5 s. Each wheel has a radius of 0.60 m and is rotating in a counterclockwise (positive) directions. What is (a) the constant angular acceleration (in rad/s2) and (b) the angular displacement (in rad) of each wheel?

Explanation:

Given that,

A motorcycle, which has an initial linear speed of 5.0 m/s, decelerates to a speed of 3.5 m/s in 4.5 s. Each wheel has a radius of 0.60 m and is rotating in a counterclockwise (positive) directions.

Angular acceleration,

Put all the values,

Angular displacement,

Hence

(a) The angular acceleration is - 0.56 rad/s^2.

(b) The angular displacement is 31.6 rad.

Explanation:

initial velocity, u = 5 m/s

final velocity, v = 3.5 m/s

radius, r = 0.6 m

time, t = 4.5 s

initial angular velocity, wo = u/r = 5/0.6 = 8.33 rad/s

final angular velocity, w = v/r = 3.5 / 0.6 = 5.83 rad/s

(a) Use the first equation of motion to fine the angular acceleration.

(b) Use third equation of motion to find the angular displacement

half of a circle

explanation:

the arrow and the top of the circle is matching together. it is not a polygon because a polygon would always be the same shape. therefore, an half of a circle is called semicircle so you would find the radius of it.