# Uniform centripetal acceleration

• Panix
In summary, a 3.0kg ball is attached to a 1.40m string and revolves uniformly in a circle on a frictionless horizontal surface at a rate of 2 revolutions per second. To find the centripetal acceleration, use the equation ac = v^2/r, and to find the tension exerted on the string, use the equation Fc = ma = m(4pi^2r/T^2). The value of T is 0.5, and the velocity can be found by determining the distance the ball covers in one revolution.
Panix

## Homework Statement

A small ball with a mass of 3.0kg revolves uniformly in a circle on a frictionless horizontal surface. The ball is attached to a string of 1.40m to a pin set at center of circle. The object makes 2rev/sec.

a)find the centripetal accel
b)find the tension exerted on the string

## Homework Equations

ac=v^2/r
Fc= ma=m(4pi^2r/T^2)
T= .5

## The Attempt at a Solution

if its uniform wouldn't the Fc=FT(force of tension)
T would =.5 because 2 rev/1 sec?
I am not sure how to find centripetal accel because i do not know how to find the velocity unless i am missing something..

Last edited:
If it makes one revolution and the string is 1.40 m, how much distance does it cover?

Firstly, to find the centripetal acceleration, we can use the equation ac = v^2/r, where v is the velocity and r is the radius of the circle. In this case, v can be found by dividing the number of revolutions (2 rev/sec) by the time period of one revolution (T= 0.5 sec), giving us a velocity of 4 m/s. Plugging this into the equation, we get ac = (4 m/s)^2 / 1.4m = 11.43 m/s^2.

To find the tension exerted on the string, we can use the equation Fc = ma, where m is the mass of the ball and a is the centripetal acceleration we just calculated. Plugging in the values, we get Fc = (3.0 kg)(11.43 m/s^2) = 34.3 N.

In summary, the centripetal acceleration of the ball is 11.43 m/s^2 and the tension exerted on the string is 34.3 N. It is important to note that these values are only accurate if the ball is truly revolving uniformly and there is no friction present.

## 1. What is uniform centripetal acceleration?

Uniform centripetal acceleration is the acceleration experienced by an object moving in a circular path at a constant speed. It always points towards the center of the circle and is necessary to keep the object moving in a curved path.

## 2. How is uniform centripetal acceleration measured?

Uniform centripetal acceleration can be measured using the formula a = v^2/r, where a is the acceleration in meters per second squared, v is the speed in meters per second, and r is the radius of the circular path in meters.

## 3. What causes uniform centripetal acceleration?

The force of gravity or tension in a string is typically responsible for causing uniform centripetal acceleration. This force constantly pulls the object towards the center of the circle, causing it to accelerate.

## 4. Is uniform centripetal acceleration the same as uniform circular motion?

No, they are not the same. Uniform circular motion refers to the motion of an object moving in a circular path at a constant speed, while uniform centripetal acceleration refers to the acceleration experienced by an object moving in a circular path at a constant speed.

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

Some examples of uniform centripetal acceleration in everyday life include a car making a turn on a curved road, a satellite orbiting the Earth, or a roller coaster moving around a loop. Any object moving in a circular path at a constant speed experiences uniform centripetal acceleration.

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