What Is Centripetal Force?

In classical mechanics, centripetal force is the combined external force that points to the center of the circle (center of curvature) when an object moves along a circular or curved orbit. The term "centripetal force" is named after the effect of this external force. This effect can be produced by any one of the forces of elasticity, gravity, friction, etc., or it can be provided by the sum of several forces or their component forces.

In classical mechanics, centripetal force is the combined external force that points to the center of the circle (center of curvature) when an object moves along a circular or curved orbit. The term "centripetal force" is named after the effect of this external force. This effect can be produced by any one of the forces of elasticity, gravity, friction, etc., or it can be provided by the sum of several forces or their component forces.

Because circular motion is a curved motion, objects in circular motion will also be subject to a combined external force acting in a different direction from their velocity. For an object in a circular motion, the centripetal force is a pulling force, and its direction changes continuously as the object moves in a circular orbit. This tensile force points to the center of the circle along the radius of the circle, hence the name "centripetal force". The centripetal force points to the center of the circle, and the object controlled by the centripetal force moves along the direction of the tangent line, so the centripetal force must be perpendicular to the direction of movement of the controlled object, and only produces acceleration in the direction of the velocity normal. Therefore, the centripetal force only changes the moving direction of the controlled object, and does not change the speed of the movement, even in non-uniform circular motion. In non-uniform circular motion, the tangential acceleration that changes the motion rate is not generated by the centripetal force.

The magnitude of the centripetal force is closely related to the mass (m) of the object, the length (r) of the circular radius of the object's movement, and the angular velocity ().

Chinese name

Centripetal force

Foreign name

centripetal force

expression

F = M²r

Applied discipline

physical

Scope of application

Mechanics, kinematics

Scope of application

mechanical

Centripetal force formula

The centripetal force F required when an object with mass m moves at a speed v along a curve with a radius of curvature r is:

Where: v is the linear velocity unit m / s, is the angular velocity unit rad / s, m is the mass unit of the object kg, r is the unit of the radius of motion of the object m, T is the unit of circular motion cycle s, and f is the frequency of circular motion unit Hz , N is the unit of rotation speed (ie frequency) of the circular motion, r / s.

In a particle accelerator, the speed of particles is close to the speed of light in a vacuum. Considering the relativistic effect, the expression of centripetal force is:

among them

For the Lorentz factor:

Centripetal Knowledge

(1) Centripetal force is named according to the effect of force. Because it generates acceleration that points to the center of the circle, it is called centripetal force. It is not a certain type of force of a definite nature. Conversely, forces of any nature can be used as centripetal forces. In fact, it can be a force of a certain nature, or a component of a certain force, or a combined external force of several forces of different properties pointing along the radius to the center of the circle.

(2) Why doesn't the centripetal force pull the object towards the center of the circle?

For a circular motion object, the speed direction must be changed all the time. In order to change the speed direction of the object, a certain amount of force is required. Imagine that the object is not subject to force. Will it not fly out along the tangent direction under the action of inertia? And the magnitude of the centripetal force when the object moves in a circle

Centripetal force (4 photos)

It is exactly equal to the required force, so it has no "residual force" to pull the object toward the center of the circle. In fact, if the given pulling force is greater than the required centripetal force, it will indeed pull the object towards the center of the circle, and if the given force is less than the required centripetal force, there will be a partial velocity in the horizontal tangent direction, so that the moving object will do Curved motion deviating from a circular orbit.

(3) Uniform circular motion (curve motion) is a variable speed motion

The velocity direction of a uniform circular motion changes at all times, and there must be acceleration. From the perspective of kinematics, it can be proved that the acceleration of an object doing uniform circular motion is a = v² / r = 2r, and the direction always points to the center of the circle. Therefore, the acceleration of uniform circular motion is called centripetal acceleration. The centripetal acceleration is always perpendicular to the velocity. Only the direction of the linear velocity is changed, and the magnitude of the linear velocity is not changed. The direction is the same as the centripetal force and points to the center of the circle.

(3) Is there any centrifugal force?

Centrifugal force is a manifestation of inertia, which does not actually exist. In order for the object to make a circular motion, the object needs to be subjected to a force pointing to the center of the circle-that is, a centripetal force. If you use this object as the origin to establish coordinates, it looks like there is a force in the same direction as the centripetal force, which moves the object away from the center of the circular motion. (When the force of the object is not enough to provide the centripetal force required for circular motion, it looks as if the centrifugal force is greater than the centripetal force. The object will move away from the center of the circle. This phenomenon is called "centrifugal phenomenon.")

It is assumed that if centrifugal force is present, it will be balanced with centripetal force, the object will be balanced by force, the speed direction will not change, it is in a balanced state, and it is impossible to perform circular motion. .

Centripetal force classification

Uniform and non-uniform circular motion

The circular motion can be divided into two types: uniform circular motion and non-uniform circular motion according to whether the speed changes.

For an object that moves in a uniform circular motion, the speed does not change, but the direction changes. Therefore, the acceleration always points to the center of the circle and its size does not change; the combined external force always points to the center of the circle and the size does not change.

An object that does non-uniform circular motion changes both in velocity direction and magnitude. In addition to acceleration pointing to the center of the circle, there is also acceleration along the tangent direction, so the combined acceleration does not point to the center of the circle, and the combined external force does not point to the center of the circle. Centripetal addition

Centripetal force (16 photos)

Velocity a = v² / r changes with v, and centripetal force a changes with F = ma. For example, the ball moves along a smooth circular orbit in a vertical plane. As shown in the figure, the ball is subjected to two forces when passing through point A from top to bottom, where the direction of gravity G is the same as Va, which makes the speed of the ball occur. The orbital spring force N is perpendicular to Va and points to the center of the circle, so that the velocity direction of the ball changes, that is, to provide the centripetal force of the ball to make a circular motion. The resultant force F is at an angle with Va and does not point to the center of the circle.

Variable speed circular motion

Centripetal force is not constant ^[1]

In uniform circular motion, the combined external force does not change the magnitude of the linear velocity, but only changes the direction of the linear velocity. The centripetal force is the combined external force on the object. In the variable-speed circular motion, the combined external force must change the magnitude of the linear velocity on the one hand. To change the direction of the linear velocity, the centripetal force is not necessarily equal to the combined external force on the object, and the magnitude of the centripetal force in the variable-speed circular motion is not constant because the linear velocity of the variable-speed circular motion is not constant.