# Angular Velocity & Acceleration for a Series of Connected Objects

• Mandex Chak
In summary, the conversation discusses how to find the total angular velocity and acceleration of a rotating disk with two arms (AD and DB) and a small z axis. The disk is rotating at a rate of 1500 rpm and the arms are rotating in the ZY plane at rates of 0.2 rad/s^2 and -0.3 rad/s^2. The length of the arms is given. The solution involves calculating the total angular acceleration and using the formula W = w(of the rotating disk) + w(B/D) + w(D/A). There is also mention of linear velocity, but it is not clear how it is related to the problem.
Mandex Chak
1.
A rotating disk is connected with two arms AD and DB which are rotating with the rate of 0.2 rad/s^2 and -0.3 rad/s^2 respectively about X or x' axis. Disk itself is rotating about small z axis with the rate of 1500 rpm.

AD and DB is rotating in ZY plane. Small z co-insides with DB arm. X and x are parallel. Length of the AD and DB is given.

Now how I should approach this problem to find the total angular velocity and acceleration of the disk with respect to the inertial co-ordinate system XYZ2. 3. So far what I think of the solution:
Total Angular Acceleration, w:
W = w(of the rotating disk) + w(B/D) + w(D/A)
Velocity V(B/A) = (V)Rel + (W * ( Position Vector R(B/A) ) )

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Mandex Chak said:
Total Angular Acceleration, w:
W = w(of the rotating disk) + w(B/D) + w(D/A)
Is that what you meant? w is more normally used (substituting for Greek ω) to mean angular velocity. α is used for angular acceleration.
Mandex Chak said:
Velocity V(B/A) = (V)Rel + (W * ( Position Vector R(B/A) ) )
That reads more like you are discussing linear velocity (referring to points B, A), not angular velocity.

## What is angular velocity?

Angular velocity is the rate of change of angular displacement, or the speed at which an object is rotating around a fixed axis. It is measured in radians per second (rad/s) or degrees per second (deg/s).

## How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It can also be calculated by multiplying the radius of the circle by the linear velocity of the object.

## What is the difference between angular velocity and linear velocity?

Angular velocity refers to the rotation of an object around a fixed axis, while linear velocity refers to the speed and direction of an object in a straight line. Angular velocity is measured in terms of angles, while linear velocity is measured in terms of distance per time.

## What is angular acceleration?

Angular acceleration is the rate of change of angular velocity, or the change in the speed at which an object is rotating around a fixed axis. It is measured in radians per second squared (rad/s2) or degrees per second squared (deg/s2).

## How is angular acceleration related to angular velocity?

Angular acceleration and angular velocity are directly related. When angular acceleration is positive, the angular velocity increases, and when angular acceleration is negative, the angular velocity decreases. A constant angular acceleration results in a linearly increasing or decreasing angular velocity.

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