Centripetal Forces

a greater linear speed for the vehicle. The linear velocity is the radius of the tire multiplied by the angular speed. The angular velocity has just two directions: clockwise or counterclockwise, while linear velocity is considered tangent to the path.

CENTRIPETAL FORCES

So far, we have talked about acceleration as an increase or decrease in velocity, which can change in magnitude, direction, or both. Because the direction of the linear velocity is changing all the time, so will the direction of its acceleration, even though the velocity may be the same over time. This is experienced when going around a corner; there is a sideways acceleration noted. Can this acceleration be quantified? It turns out that it can.

Acceleration in a circle points directly into the center of the circle or toward the center of the circular path. This is referred to as the centripetal acceleration. How can you show this center-seeking acceleration using vectors? Remember that velocity is a vector and acceleration is a vector. If you look at a circle with two different velocities (that have the same magnitude but different direction), the change in velocity is going to point toward the circle’s center. If acceleration is the change in velocity over the change in time, this vector will be larger if the velocity is larger. Figure 24 shows the direction and calculation of centripetal acceleration:

Figure 24.