Calculate Velocity/Acceleration from Angular Vel/Acc & Radius of Disk

[looseliver]

Homework Statement

How do i calculate the velocity and accaleration of a point on a moving disk when i know the angular velocity , angular acceleration and radius of the disk?

Homework Equations

angular velocity 8k rad/s
angular acceleration -10k rad/s2
Radius 0.5m

The Attempt at a Solution

 

[radou]

What you wrote under "Relevant equations" actually belongs into the "Homework Statement " part. So, what are the relevant equations?

 

[looseliver]

Sorry about that. this is my first post.

The relevant equations is what i am unsure about...
I am considering using:
v=wr
Velocity = angular velocity x Radius

and:
a=xr
Acceleration = angular velocity x Radius.

I'm not certain if these are the correct equations to use. Just seems a bit straight forward.

 

[radou]

You got the first relation right, but not the second one. The acceleration of the point equals angular acceleration times the radius.

 

[DeeNos]

To calculate the velocity and acceleration of a point on a moving disk, we can use the following equations:

Velocity (v) = radius (r) * angular velocity (ω)
Acceleration (a) = radius (r) * angular acceleration (α)

Substituting the given values, we get:

Velocity (v) = 0.5m * 8k rad/s = 4m/s
Acceleration (a) = 0.5m * (-10k rad/s2) = -5m/s2

Therefore, the velocity of the point on the disk is 4m/s and the acceleration is -5m/s2. It is important to note that the acceleration is negative, indicating that the point is experiencing a deceleration or slowing down in its motion. This could be due to friction or other external forces acting on the disk.