Modiefied Atwood Machine Problem.

[Ogir28]

1. 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.


2. Homework Equations

(tangential speed) v= rw
(angular speed) w=v/r or 2π/t
(tangential acceleration) = r * (change in w/ change in t)
(angular accel.) =change in w/ change in t

The Attempt at a Solution

I know that the further a point is from the center, the faster its velocity.
the closer a point is to the center, the slower its velocity.
Therefore, the magnitude will always be greater at point A?
I think Point a = r(radius) and point B= 1/2r...
I don't know how to approach the problem...

 

[rl.bhat]

When the wheel is moving every particle on the wheel describes the same angle at the center. Then what happen to the angular speed?
The tangential velocity has the same magnitude but it changes the direction. Then what happens to the tangential speed?
Proceed in the same manner for other quantities.

 

[nlightner]

I would approach this problem by analyzing the equations and understanding the concepts of angular and tangential motion. Firstly, we know that the angular speed of a rotating object is directly proportional to its tangential speed, which is given by the equation v= rw. This means that as the angular speed increases, the tangential speed will also increase.

Now, looking at point A and B, we can see that point A is further from the center of the wheel compared to point B. Using the equation for angular speed, w=v/r, we can see that the angular speed will be greater at point A since it has a larger radius. This also means that the tangential speed will be greater at point A.

Moving on to angular acceleration, we can use the equation for tangential acceleration, a=r*(change in w/change in t), to understand its relationship with angular acceleration. Since point A has a larger radius, the tangential acceleration will be greater at point A. Similarly, the centripetal acceleration, which is given by the equation a=v^2/r, will also be greater at point A due to its larger radius.

In conclusion, the magnitude of all the quantities mentioned (angular speed, tangential speed, angular acceleration, tangential acceleration, and centripetal acceleration) will be greater at point A compared to point B due to its larger radius. This is because the angular and tangential motion of a rotating object is directly proportional to its radius.