i have a question in my book
centripetal acceleration = r^-1 v^2
ok I agree
but in my book acceelration is labeled as a vector but yet the velocity is not...
Why?
By v it means the component of the V vector that is tangent to the circle of radius r.
It identifies the centripetal acceleration as an inward pointing vector because the author wants to make sure you know that centripetal acceleration has a direction, namely toward the center.
The reason why acceleration is labeled as a vector, while velocity is not, is due to the nature of their respective quantities.
Velocity is a vector quantity because it includes both magnitude (speed) and direction. In other words, velocity not only tells you how fast an object is moving but also in which direction it is moving. Since velocity takes into account direction, it must be represented as a vector with both magnitude and direction.
On the other hand, acceleration is defined as the rate at which an object's velocity changes. Acceleration can occur in multiple directions, including changes in speed, changes in direction, or both. As a result, it is necessary to represent acceleration as a vector since it provides information about both the magnitude and direction of the change in velocity.
In the case of the formula you mentioned, "centripetal acceleration = r^-1 v^2," the equation shows that the centripetal acceleration is directly proportional to the square of the velocity (v) and inversely proportional to the radius (r). The negative exponent on the radius indicates that the centripetal acceleration vector is directed inward, towards the center of motion. By considering acceleration as a vector, this equation provides us with valuable information about the direction and magnitude of the centripetal acceleration.