Rotational Kinematics of a disk

[Batman4t]

Homework Statement

A disk with a radial line painted on it is mounted on an axle perpendicular to it and running through its center. It is initially at rest, with the line at q0 = -90.0°. The disk then undergoes constant angular acceleration. After accelerating for 3.15 s, the reference line has been moved part way around the circle (in a counterclockwise direction) to qf = 130°.

Given this information, what is the angular speed of the disk after it has traveled one complete revolution (when it returns to its original position at -90.0°)?

Homework Equations

http://www.ajdesigner.com/phpcircularmotion/centripetal_acceleration_equation.php

The Attempt at a Solution

Not sure I know have to use Rotational Kinematics to find the angular velocity first.

 

[Shooting Star]

You have to use only the eqns of Rotational Kinematics, not dynamics.

 

[Moetasim]

Rotational Kinematics is a branch of physics that deals with the motion of rotating objects. It involves concepts such as angular displacement, angular velocity, and angular acceleration. In this case, we can use the equation:

θf = θ0 + ω0t + 1/2αt^2

Where:
θf = final angular position (130°)
θ0 = initial angular position (-90°)
ω0 = initial angular velocity (unknown)
t = time (3.15 s)
α = angular acceleration (unknown)

We can rearrange the equation to solve for ω0:

ω0 = (θf - θ0 - 1/2αt^2)/t

Substituting in the known values, we get:

ω0 = (130° - (-90°) - 1/2α(3.15 s)^2)/3.15 s

Simplifying, we get:

ω0 = (220° - 1.575α)/3.15 s

Now, to find the angular speed after one complete revolution, we can use the equation for angular speed:

ω = Δθ/Δt

Since one complete revolution is 360°, we can substitute these values into the equation:

ω = 360°/t

Substituting in the known value of t (3.15 s), we get:

ω = 360°/3.15 s = 114.286°/s

Therefore, the angular speed of the disk after one complete revolution is 114.286°/s.