# Angular velocity/acceleration problem

• NewbEngineer
In summary: A in terms of B.In summary, if disc A and B are spinning against each other without slipping or translating, the angular velocity and angular acceleration of disc A will be three times less than that of disc B. This is because disc A has a diameter of 3D while disc B has a diameter of D. No other conclusions can be made about the motion of disc A in relation to B.
NewbEngineer
Suppose disc A and B are spinning against each other without slipping or translating. What can be said about the motion of disc A in terms of B? (select all that apply; if none apply, leave the boxes blank)
Disk A has a diameter of 3D while disk B has a diameter of D

a. Angular velocity magnitude of A will be 3 times greater than B

b. Angular velocity magnitude of A will be equal to B

c. Angular velocity magnitude of B will be 3 times greater than A

d. Angular acceleration magnitude of A will be 3 times greater than B

e. Angular acceleration magnitude of A will be equal to B

f. Angular acceleration magnitude of B will be 3 times greater than A

L= Iw angular momentum = moment of inertia x angular velocity
t=Ia torque = moment of inertia x angular acceleration

Seeing from the question I think at the moment of contact, the velocity would be 0. But if we are looking at angular velocity as a whole, disk A should have 1/3 the speed of disk B. If that's the case then the angular acceleration diffeence would've also been 3 times between A and B. Can someone verify it?

$$3w_A = w_B , \ \ \ 3\alpha_A = \alpha_B$$

there's nothing else

## 1. What is angular velocity/acceleration?

Angular velocity is the rate of change of angular displacement over time, while angular acceleration is the rate of change of angular velocity over time. It is commonly used to describe the rotation of an object around an axis.

## 2. How is angular velocity/acceleration calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time, while angular acceleration is calculated by dividing the change in angular velocity by the change in time. Both are typically measured in radians per second (rad/s) or radians per second squared (rad/s^2) respectively.

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

Angular velocity is a vector quantity that describes the rotational speed and direction of an object, while linear velocity is a vector quantity that describes the speed and direction of an object in a straight line. Both are measured in different units (rad/s vs. m/s), and angular velocity depends on the radius of the object's rotation, while linear velocity does not.

## 4. How does angular velocity/acceleration affect an object's motion?

Angular velocity and acceleration determine the direction and rate of an object's rotation, which can affect its overall motion. For example, a higher angular velocity will result in a faster rotation, while a higher angular acceleration will result in a more rapid change in the rotational speed. These factors can also influence an object's stability and tendency to maintain its rotational motion.

## 5. How are angular velocity/acceleration problems typically solved?

Angular velocity/acceleration problems are typically solved using the equations for angular velocity and acceleration, along with other relevant equations such as torque and moment of inertia. It is important to carefully consider the given values and units, and to use the correct formulas in order to arrive at the correct solution.

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