# Centripetal Acceleration Question

In summary: Then you can solve for ##a_c##.In summary, in this conversation, the participants discuss the concept of centripetal acceleration in relation to a simple pendulum. They determine that the sum of forces acting on the object is equal to the centripetal acceleration, which is not a force but an acceleration. They also discuss the importance of correctly setting up the equation for Newton's second law in order to solve for the magnitude of the centripetal acceleration.
An object weighing 4 Newtons swings on the end of a string as a simple pendulum. At the bottom the swing, the tension in the string is 6 Newtons. What is the magnitude of the centripetal acceleration of the object at the bottom of the swing.Centripetal Acc. = v^2/r Sum of forces = T+Ac=mg?Attempt

-T-mg=Ac?
-6-4 = Ac
I don't know where to go from here.

Newton's second law says
$$\sum \vec{F}_i = m\vec{a}.$$ The centripetal acceleration is not a force. It's an acceleration. It goes into the righthand side of F=ma. The tension and the weight go into the lefthand side. Try again and pay attention to the sign of T and mg when summing the forces.

vela said:
Newton's second law says
$$\sum \vec{F}_i = m\vec{a}.$$ The centripetal acceleration is not a force. It's an acceleration. It goes into the righthand side of F=ma. The tension and the weight go into the lefthand side. Try again and pay attention to the sign of T and mg when summing the forces.

So I set it up as Sum of forces = T-mg=Ac
6-4=Ac
2?

Closer. The lefthand side is correct, but the righthand side isn't. You can't add up a bunch of forces and then set the result to something that isn't a force. ##a_c## is the centripetal acceleration; it's not a force. It's the ##a## in ##ma## on the righthand side.

vela said:
Closer. The lefthand side is correct, but the righthand side isn't. You can't add up a bunch of forces and then set the result to something that isn't a force. ##a_c## is the centripetal acceleration; it's not a force. It's the ##a## in ##ma## on the righthand side.

so is it 2=mAc
so its 2 g ? the answer choices only come in a number times g

Not quite. You need to figure out what the mass of the object is from its weight.

## What is centripetal acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path that an object experiences when it is moving in a circular motion.

## What is the formula for calculating centripetal acceleration?

The formula for centripetal acceleration is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

## How does centripetal acceleration differ from regular acceleration?

Regular acceleration, or linear acceleration, is the change in velocity of an object in a straight line. Centripetal acceleration, on the other hand, is always directed towards the center of a circular path and keeps the object moving in a circular motion.

## What factors affect centripetal acceleration?

The factors that affect centripetal acceleration include the speed of the object, the radius of the circular path, and the mass of the object. As the speed and radius increase, the centripetal acceleration also increases. A larger mass will also result in a larger centripetal acceleration.

## What are some real-life examples of centripetal acceleration?

Some real-life examples of centripetal acceleration include a car turning around a curve, a rollercoaster moving around a loop, and a satellite orbiting around the earth. Any object that moves in a circular path experiences centripetal acceleration.

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