# Normal force as centripetal force

• Telemachus
In summary, the problem involves a particle of mass m resting on a frictionless sphere of radius R, and finding the value of the angular coordinate at the instant the particle leaves the surface. The initial approach of setting N-mg\cos\theta=0\Rightarrow{N=mg\cos\theta} is questioned due to inertia, but the concept of conservation of energy is suggested as a way to find the speed of the particle at an angle theta. The forces involved can be separated into perpendicular and tangential components using a picture. There may also be a "kinematic" solution using polar coordinates.
Telemachus

## Homework Statement

Hi. I have this problem:

A particle of mass m, rests on top of a frictionless sphere of radius R. Admitting that part from the rest for the position indicated in the figure along a path contained in a vertical plane.
Get the value of the angular coordinate at the instant the body leaves the surface of the sphere.

In the first place I thought: $$N-mg\cos\theta=0\Rightarrow{N=mg\cos\theta}$$
And then $$N=0\Leftrightarrow{mg\cos\theta=0}\Leftrightarrow{\cos\theta=0}\Leftrightarrow{\theta=\frac{\pi}{2}}$$

But now I'm not sure about this. I think that the angle could be before $$\theta=\frac{pi}{2}$$, because of the inertia. But I don't know how to raise the problem this way.

Bye there.

#### Attachments

• sphere.PNG
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The first step is finding out what the speed of the particle at an angle theta is. Conservation of energy is the easiest way to find that.

The normal force and the force of gravity must together produce the acceleration of the mass. Draw a picture of the forces involved. You can separate the forces and accelerattions in a component that is perpendicular and one that is tangential to the surface.

I haven't worked yet with conservation of energy, but I see what you're trying to tell me. Then just supposing that the normal force is zero when $$cos\theta=0$$ its wrong, right?

There is a "kinematic" way of doing this? with polar coordinates maybe?

Thanks for posting willem2.

## 1. What is the concept of normal force as centripetal force?

The normal force as centripetal force is a concept in physics that describes the force exerted by a surface on an object in circular motion, towards the center of the circle. It is also known as the centripetal force, as it is responsible for keeping an object moving in a circular path.

## 2. How is normal force related to centripetal force?

The normal force is directly related to the centripetal force in circular motion. The normal force is the component of the force exerted by a surface on an object that is perpendicular to the surface. In the case of circular motion, this perpendicular force acts towards the center of the circle, thus serving as the centripetal force.

## 3. Can normal force act as centripetal force in all cases?

No, the normal force cannot always act as the centripetal force. In order for the normal force to act as the centripetal force, the object must be in contact with a surface that is perpendicular to the direction of motion. If the object is not in contact with such a surface, then another force, such as tension or gravity, must act as the centripetal force.

## 4. How is the magnitude of normal force as centripetal force determined?

The magnitude of the normal force as centripetal force can be determined using the equation Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular motion. The normal force will have the same magnitude as the centripetal force, but in the opposite direction.

## 5. What are some real-life examples of normal force as centripetal force?

Some examples of normal force as centripetal force include a car driving around a curved road, a satellite orbiting around a planet, and a rollercoaster moving along a circular track. In all of these cases, the normal force from the surface is acting as the centripetal force that keeps the objects moving in a circular path.

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