What Is Centripetal Force?

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What is centripetal force?

Whenever anything is rotating, that body is experiencing a force. Namely, it is experiencing what is called centripetal force. If you tie a ball onto a string and spin it around, this force keeps it from flying away.

Remember Newton’s First Law of Motion: An object at rest will stay at rest until acted upon by an external net force. An object in motion will remain in motion unless acted upon by an external net force. This is also called the law of inertia.

Let’s focus on the second part of the law. As the balls rotates, it tends to continue going straight. When the string snaps, the ball continues going straight from the point it was released. At every point in the ball’s rotational motion, it has a linear, or tangential, velocity. This defines the speed and direction that the ball would travel upon release. The ball tends to remain in this straight motion; however, a force is keeping it from escaping. This is where centripetal force comes in.

Centripetal force is the force which pulls the ball toward the center of rotation. The ball wants to keep going straight, but this force tugs at it to continue rotating. The force to keep the ball in rotational motion increases the farther away it is from the center.

Some examples

On a merry-go-round, your body wants to fly off but you want to stay on. So, you hold onto the bars to overcome your body’s natural resistance to fly off (inertia). The farther away from the center you are, the harder you have to hold onto the bar to stay on. As you pull on the bar, it pulls back on you with an equal centripetal force.

This same force is applicable to anything going in a circle, from turning a corner in a car to the Moon orbiting the Earth. As the car turns, your body wants to fly out, but the car exerts a force on you to keep you rotating. Gravity acts as the centripetal force keeping the Moon from flying out of orbit with Earth.

Centripetal force is also essential in keeping a roller-coaster cart moving through a loop-the-loop. At the top of the loop, the gravitational and normal forces combine. The normal force is the force the cart pushes against you. Gravity pulls and the normal force pushes the cart downward. The cart needs a sufficient centripetal force to balance these out. It enters the loop-the-loop with a high enough velocity to balance these forces out and prevent the cart from rolling backwards.

Equations

If it’s easier for you to see these relationships using equations, here are some to help you out. Just remember that the equations represent the physics-not the other way around.

v_r=r\omega

F_c=\frac{mv_r^2}{r}

Where v_r is tangential velocity, r is the rotational radius, \omega is the angular velocity, and F_c is the centripetal force. This relationship can be shown by noting that:

F_c=ma_c

a_c=\frac{v_r^2}{r}

Where a_c is the centripetal acceleration. The direct relationship between force and radius is better shown by substituting r\omega for v_r in the second equation:

F_c=mr\omega^2

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