# What is the centripetal acceleration?

In summary, the question is asking for the centripetal acceleration provided by the string when a ball is twirled in a circle and then released, making an angle of 30 degrees from the horizontal and covering a distance of 1,000m before hitting the ground. To find the centripetal acceleration, we need to know the velocity of the ball, which can be obtained by working backwards from the given distance and angle. This velocity is equivalent to the velocity of the object as it spins around the circle.

## Homework Statement

If a ball is being twirled in a circle with a radius of 0.5m, and then is let go such that the balls velocity makes an angle 30 degrees from the horizontal and then covers a distance of 1,000m before it hits the ground. What was the centripetal accelertaion provided by the string??

Picture provided

Ac = v^2 / r

## The Attempt at a Solution

I don't really understand how to get the velocity in order to just plug in everything else into the equation.

Last edited:
Work backwards. What velocity would you need to make the ball arc 30 and cover 1000m for instance.

QuarkCharmer said:
Work backwards. What velocity would you need to make the ball arc 30 and cover 1000m for instance.

I'm still not understanding it.

He's saying pretend there was just a projectile fired at a 30 degree angle that covered 1000m, from that you can find the velocity of the projectile, that velocity is the same as the velocity the object was moving as it spun around the circle.

The centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is given by the equation Ac = v^2 / r, where v is the velocity of the object and r is the radius of the circle.

In this scenario, the ball is being twirled in a circle with a radius of 0.5m. When it is let go, its velocity is not given directly, but we can calculate it using the distance it covers and the angle at which it is released. This can be done using trigonometry:

v = d/t = 1000m / t

Where t is the time taken for the ball to travel 1000m. To find t, we can use the fact that the angle between the ball's initial velocity and the horizontal is 30 degrees, and the distance traveled is the arc length of the circle. This gives us:

t = (theta * r) / v = (30 degrees * 0.5m) / v = 0.2618 / v

Now we can substitute this value of t into the equation for velocity to get:

v = 1000m / (0.2618 / v) = 3823.7 m/s

Now we can plug this value into the equation for centripetal acceleration to get:

Ac = (3823.7 m/s)^2 / 0.5m = 2,919,379 m/s^2

Therefore, the centripetal acceleration provided by the string is approximately 2,919,379 m/s^2.

## 1. What is the definition of centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and is responsible for keeping the object moving in a circular motion.

## 2. How is centripetal acceleration different from normal acceleration?

Normal acceleration is the rate of change of an object's velocity in a straight line, while centripetal acceleration is the rate of change of an object's direction in a circular path. Normal acceleration is always tangential to the circular path, while centripetal acceleration is always directed towards the center of the circle.

## 3. 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. This formula can also be written as a = ω^2r, where ω is the angular velocity of the object.

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

Some examples of centripetal acceleration in everyday life include the motion of a car around a curved road, the rotation of a Ferris wheel, and the movement of a ball attached to a string when swung in a circle.

## 5. How does centripetal acceleration relate to centripetal force?

Centripetal acceleration and centripetal force are directly related, as they both act towards the center of the circle and are responsible for keeping an object in circular motion. The centripetal force is the force that causes the centripetal acceleration.

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