# Change in magnitude of radial acceleration

• alexmahone
In summary, the magnitude of radial acceleration is calculated by dividing the square of the object's speed by the radius of the circular path it is following. This change in magnitude is affected by the object's speed, radius, and mass, and it directly impacts the direction of the object's motion. The magnitude of radial acceleration can be negative, but the acceleration vector always points towards the center of the circle. Additionally, the magnitude of radial acceleration is directly proportional to the centripetal force acting on an object.
alexmahone

## Homework Statement

A wheel changes its angular velocity with a constant angular acceleration while rotating about a fixed axis through its center. Show that the change in the magnitude of the radial acceleration during any time interval of a point on the wheel is twice the product of the angular acceleration, the angular displacement, and the perpendicular distance of the point from the axis.

## Homework Equations

$$a_r=\omega^2 r$$

## The Attempt at a Solution

Got it, never mind.

## 1. How is the magnitude of radial acceleration calculated?

The magnitude of radial acceleration is calculated by dividing the square of the object's speed by the radius of the circular path it is following. This can be represented by the formula a = v^2/r, where a is the magnitude of radial acceleration, v is the speed, and r is the radius.

## 2. What factors affect the change in magnitude of radial acceleration?

The change in magnitude of radial acceleration is affected by the speed of the object and the radius of the circular path it is following. It is also affected by the mass of the object, as a heavier object will require a greater force to change its direction of motion.

## 3. How does the change in magnitude of radial acceleration impact an object's motion?

The change in magnitude of radial acceleration directly affects the direction of an object's motion. If the magnitude of radial acceleration increases, the object's motion will curve more sharply towards the center of the circle. If the magnitude decreases, the object's motion will curve less sharply or may even move in a straight line.

## 4. Can the magnitude of radial acceleration be negative?

Yes, the magnitude of radial acceleration can be negative. This occurs when an object is slowing down or changing direction in the opposite direction of its initial motion. However, the actual acceleration vector will still be directed towards the center of the circle, as it is a centripetal force.

## 5. How is the magnitude of radial acceleration related to centripetal force?

The magnitude of radial acceleration is directly proportional to the centripetal force acting on an object. This means that as the magnitude of radial acceleration increases, the centripetal force also increases. This relationship is represented by the formula F = ma = mv^2/r, where F is the centripetal force, m is the mass of the object, and a is the magnitude of radial acceleration.

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