As the ball moves around the circle, the centripetal force is continually causing the direction of the ball’s velocity to change. The centripetal acceleration measures the rate at which the direction of the ball’s velocity is changing. If you go to the website below you can see how the centripetal acceleration is related to the change of the direction of the velocity. http://hyperphysics.phy-astr.......
Force and acceleration are vectors. A vector has magnitude and direction. The centripetal force does not change the magnitude of the ball’s velocity. The centripetal force does change the direction of the ball’s velocity. As the ball moves around the circle, the centripetal force is continually causing the direction of the ball’s velocity to change. The centripetal acceleration measures the rate at which the direction of the ball’s velocity is changing.
If you go to the website below you can see how the centripetal acceleration is related to the change of the direction of the velocity.
http://hyperphysics.phy-astr.gsu.edu/hba…
A ball is rolling in a circle with a constant velocity of 5m/s. The radius of the circle is 5m.
a = v^2/r = 25m^2/s^2/5m = 5 m/s^2
See your problem is that you are memorizing the shorthand without understanding the physics it's describing. Learn the physics, then derive the equations; that way, at least, you'll know what those equations are telling you in shorthand.
Here's the physics. Inertia. The momentum P = mV of a body will not change unless acted on by some force over a period of time. So when a body is FORCED to turn, like to change directions, to turn, it takes a force to change that momentum, And we call that force, the centripetal force, as it's forcing inward toward the turn axis.
That's the physics. Now the shorthand to say the same thing, but shorter and more exactly.
dP = m dV = m (dVt + dVr) = F dT where in vector notation the velocity V = Vt + Vr = tangential speed + radial speed. So we can write the average force F = m (dVt/dT + dVr/dT) = m (At + Ar) where At is the tangential acceleration At = a R; where a is the angular acceleration and R is the radius of gyration.
NOTE: In your problem, with the V = 5 mps constant speed, there is no tangential acceleration as dVt/dT = 0 = At. That is, the linear speed 5 mps is fixed.
