Magnitude of Angular Acceleration

[tag16]

Homework Statement

A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2π rad/s. After the disk rotates through 1π radians, the angular speed is 14π rad/s. What is the magnitude of the angular acceleration?

Homework Equations

w=w0+at

The Attempt at a Solution

I tried to use w=w0+at but that didn't work. What equation do I need to use?

 

[LowlyPion]

Homework Statement

A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2π rad/s. After the disk rotates through 1π radians, the angular speed is 14π rad/s. What is the magnitude of the angular acceleration?

Homework Equations

w=w0+at

The Attempt at a Solution

I tried to use w=w0+at but that didn't work. What equation do I need to use?

Consider using another equation.
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#rlin

One that doesn't involve time as a variable.

 

[nlightner]

The correct equation to use in this scenario is the formula for angular acceleration, which is α = (ωf - ωi)/t. In this case, ωi is the initial angular speed (2π rad/s), ωf is the final angular speed (14π rad/s), and t is the time it takes for the disk to rotate through 1π radians. To find the time, we can use the equation θ = ωit + (1/2)αt^2, where θ is the angle rotated (1π radians) and α is the angular acceleration. Solving for t, we get t = √(2θ/α). Substituting this into the equation for angular acceleration, we get α = (14π rad/s - 2π rad/s)/√(2(1π rad)/α). Simplifying, we get α = 12π√(2/α) rad/s^2. To find the magnitude of the angular acceleration, we can take the absolute value of this value, which is approximately 38.2 rad/s^2. Therefore, the magnitude of the angular acceleration is 38.2 rad/s^2.