# Centripetal acceleration: angle at which one will leave a dome

• dawn_pingpong
In summary, the conversation discusses a question and solution involving centripetal acceleration and Newton's law. The law states that the centripetal force must be the net radial force on the skater, which includes the normal force FN directed outward and the radial component of the skater's weight directed inward. This is used to solve the first part of the question and the remaining parts can be solved using vectors and projectile motion.

see attached.

## Homework Equations

centripedal acceleration: a=v^2/r

## The Attempt at a Solution

Okay I found the solution for part 1.

question 2. I know the change in energy part. But I don't really understand how

"Newton’s law states that the centripetal force must be the net radial force
on the skater, which is the normal force FN directed radially
outward, and the radial component of his weight, mg cos θ
directed inward."

and the equation that follows.

I think I can do part 2 and 3 by vectors and projectile motion once the 1st part is solved.

#### Attachments

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dawn_pingpong said:
I don't really understand how

"Newton’s law states that the centripetal force must be the net radial force
on the skater, which is the normal force FN directed radially
outward, and the radial component of his weight, mg cos θ
directed inward."

The law states F = ma, and that is also true for any projection of the vectors involved. If we take the radial projection, we end up with the quoted statement.

okay thanks now I understand. Thanks so much for always coming to my rescue!

## 1. What is 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.

## 2. How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the formula a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius of the circular path.

## 3. What does the angle at which one will leave a dome have to do with centripetal acceleration?

The angle at which one will leave a dome is related to the centripetal acceleration because it determines the direction in which the object will move when it leaves the circular path. If the angle is too steep, the object will not be able to maintain its circular motion and will leave the dome.

## 4. How does the angle at which one will leave a dome affect the speed of the object?

The angle at which one will leave a dome does not directly affect the speed of the object. However, it does affect the direction of the object's motion, which in turn can affect its speed if it encounters other forces such as friction.

## 5. What factors can affect the angle at which one will leave a dome?

The angle at which one will leave a dome can be affected by factors such as the speed of the object, the radius of the dome, and the surface of the dome (e.g. friction). Additionally, the angle can also be affected by any external forces acting on the object, such as gravity or air resistance.