I with a physics HW problem PLEase

[Ogir28]

I need help with a physics HW problem ASAP...PLEase...

A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point A is on the rim of the wheel and point B is midway between the rim and the center of the wheel. For each of the following quantities, it is the magnitude larger at A or at B, or is it the same at both points: a) angular speed, b) tangential speed, c) angular acceleration, d) tangential acceleration, and e) centripetal acceleration. Justify your answers.

I don't understand what they want me to do. There are no "givens" besides point A and point B which I think A=r and B= 1/2r

I have the formulas for the accelerations and velocities but don't know how to apply them...

 

[Jack21222]

They want you to say whether the magnitude of the listed quantities a through e is larger on the edge of the wheel or the center of the wheel.

In other words, does increasing the radius increase or decrease the magnitude of those quantities?

 

[nlightner]

I can understand that this problem may seem confusing at first. To solve this problem, we need to use the basic principles of rotational motion and apply them to the given scenario. I will walk you through the steps of solving this problem to help you understand it better.

First, let's define the given variables. As you correctly stated, point A is at the rim of the wheel and point B is at the midpoint between the rim and the center. We can also define the radius of the wheel as r, and the distance between point A and B as 1/2r.

Next, we need to understand the concepts of angular speed, tangential speed, angular acceleration, tangential acceleration, and centripetal acceleration. Angular speed is the rate at which the wheel is rotating, measured in radians per second. Tangential speed is the linear speed at which a point on the rim of the wheel is moving, measured in meters per second. Angular acceleration is the rate at which the angular speed is changing, measured in radians per second squared. Tangential acceleration is the linear acceleration of a point on the rim of the wheel, measured in meters per second squared. And finally, centripetal acceleration is the acceleration towards the center of the wheel, measured in meters per second squared.

Now let's apply these concepts to points A and B. Since point A is at the rim of the wheel, it is further away from the axis of rotation compared to point B. This means that point A has a larger radius than point B, and therefore, a larger tangential speed, tangential acceleration, and centripetal acceleration. However, the angular speed and angular acceleration will be the same at both points A and B, as they are determined by the rotation of the wheel, not the distance from the axis of rotation.

To justify these answers, we can use the equations for tangential speed, tangential acceleration, and centripetal acceleration, which are all proportional to the radius of the wheel. This means that as the radius increases, so do these quantities. On the other hand, the angular speed and angular acceleration are determined by the initial and final values of the angular speed and the change in time, not the radius.

In conclusion, the magnitude of tangential speed, tangential acceleration, and centripetal acceleration will be larger at point A compared to point B due to the larger radius. However, the magnitude of angular speed and angular acceleration will be