Because the two velocities are identical, this will lead to an isosceles triangle (which is one that has two equal sides). Based on the manipulation of knowns and equations, the centripetal acceleration is the same thing as velocity squared divided by the radius. This means that the smaller the radius, the greater is the centripetal acceleration. You can also demonstrate a relationship between the centripetal acceleration and the angular velocity. The relationship is that the centripetal acceleration is equal to the radius multiplied by the angular velocity squared. This means the centripetal acceleration is directly proportional to the radius and the square of the angular velocity.
CENTRIPETAL FORCE There can be forces that result in centripetal acceleration. A few examples, include tension on the rope attached to a tether ball and the force of gravity affecting the moon. There are also forces placed on the tube in a spinning centrifuge. What’s true is that any force that causes uniform circular motion is referred as a centripetal force. The direction of this force is in the direction of centripetal acceleration, even though these are not the same thing. This brings in Newton’s second law of motion, which states that Force equals mass times acceleration. In the case of uniform circular motion, the acceleration being referred to is the centripetal acceleration. When it relates to angular velocity, force equals mass times the radius times the square of the angular velocity. Using these equations, you can do a number of problems. Let’s try one: How do you calculate the coefficient of friction car tires need on a flat curve? This basically involves calculating the centripetal force on a car that turns a certain radius at a certain linear velocity and then calculating the static friction that will keep the tires from slipping. First, the centripetal force, which is mass times the velocity squared divided by the radius. Imagine a 900 kg car that negotiates a 500-meter radius at 25 meters per second. Doing the math, you get 900 times 25 squared divided by 500 or 1125 Newtons. Next, you need a certain coefficient of friction to prevent the car from moving out to a greater radius (spinning out of the circle). 63
