Why does curvilinear motion have to have acceleration?

Hello. The acceleration of curvilinear motion can be decomposed into tangential acceleration and normal acceleration, the tangential acceleration changes the magnitude of the velocity, and the normal acceleration changes the direction of the velocity.

The tangential acceleration is dv dt and the normal acceleration is v 2 r r is the radius of curvature at this point on the trajectory.

You ask why curvilinear motion must have acceleration, this is because the trajectory of curvilinear motion is curvilinear because the direction of velocity changes all the time, so it must have normal acceleration. So curvilinear motion must have an acceleration.

That is to say, the force of an object moving in a curve is divided into two components, one is the centripetal force, which points to the center of the circle where the radius of curvature is located, and it changes the direction of the object's motion (e.g., when this force is equal to centrifugation, it moves in a circular motion). The other component is in the same direction as the velocity, which changes the rate of motion of the object. As long as there is force, there is acceleration, so there must be acceleration in curvilinear motion:

Tangential acceleration and normal acceleration.

Assuming that curvilinear motion has no acceleration and that acceleration is zero, then according to Newton's first law, the object can only move in a straight line at a uniform velocity, and it is impossible to move in a curve. So curvilinear motion must have an acceleration.

Because if there is acceleration, it is only possible to move in a straight line at a uniform speed or in a stationary state.

The trajectory of an object's motion is the motion of a curve, which is called "curvilinear motion". When the resultant force exerted on an object is not in the same line as its velocity, the object is moving in a curve. So does the acceleration of curvilinear motion necessarily change?

1. Not necessarily. For example, in a flat throwing motion, the acceleration is the acceleration of gravity, so it does not change; But in circular motion, acceleration is constant. Curvilinear motion is divided into regular and irregular motion.

In general, regular curvilinear motion, such as circular motion, is studied. In a uniform circular motion, the magnitude of the acceleration does not change, the direction does not change, and the direction of velocity changes all the time, that is, it always follows the tangent direction of the point.

2. The acceleration in the curvilinear motion can be constant, but it does not mean that the acceleration of all the curvilinear motion is constant, and the acceleration of the uniform circular motion is directed to the direction of the center of the circle, and the resultant force is also directed to the center of the circle, which is also the change of the moment.

3. The acceleration itself is generated by the resultant external force experienced by the object, and in curvilinear motion, the direction of acceleration is always the same as the direction of the resultant external force. When the resultant external force is a constant force, the object moves in a uniform variable speed curve; When the resultant external force is a variable force, the object moves in a non-uniform variable speed curve. Acceleration is also a vector quantity, which can also be decomposed into two components, along the direction of velocity and in the direction of vertical velocity, where the component along the direction of velocity describes the speed of the change in magnitude, and the component in the direction of vertical velocity describes the speed of the change in the direction of velocity.

That's it for the question of whether the acceleration of curvilinear motion necessarily changes.

There must be an acceleration, because if you draw two vectors with different directions, there must be a difference in their vectors.

The speed of the curve is along the tangent direction of the curve, which is variable and not certain, so the velocity must change, but the acceleration does not necessarily change. For example, the acceleration of a flat throwing motion is constant, and the force is constant.

Expansion:

The acceleration in curvilinear motion can be constant, but it does not mean that the acceleration of all curvilinear motion is constant. The acceleration of a uniform circular motion is directed towards the center of the circle, and the direction changes from moment to moment, and the resultant force is also directed to the center of the circle, which also changes from moment to moment.

The trajectory of an object's motion is the motion of a curve, which is called "curvilinear motion". When the resultant force on an object is not in the same line as its velocity, the object is in curvilinear motion.

Definition of curvilinear motion

The trajectory of an object is the motion of a curve rather than a straight line, which is called "curvilinear motion".

The conditions of curvilinear motion

When the resultant force (acceleration) experienced by an object is not in the same straight line as its velocity, the object moves in a curve.

The direction of the resultant external force of the curvilinear motion

The direction of the resultant force experienced by the object moving in a curve is always directed towards the concave side of the curve.

Judgment of curvilinear motion

When judging whether an object is moving in a curvilinear way, the key is to look at the relationship between the direction of the resultant force or acceleration of the object and the direction of velocity.

The direction of the velocity of the curvilinear motion

The direction of velocity of a particle at a point in the motion of a curve is the tangent direction of this point on the curve.

No, the formula for calculating tangential acceleration is: at=dv dt.

Tangential acceleration indicates how quickly or slowly the magnitude of the velocity changes. The acceleration along the tangential direction of the track is called the tangential acceleration when the particle moves in a curvilinear motion. Its value is the rate of change of linear velocity versus time.

When it is in the same direction as the linear velocity, the linear velocity of the particle will increase, and when it is opposite to the linear velocity direction, the linear velocity of the particle will decrease. The combined vector of tangential acceleration and centripetal acceleration is the resultant acceleration of curvilinear motion.

The formula for normal acceleration is an=v 2 r.

Difference Between Tangential Acceleration and Normal Acceleration:

1. Tangential acceleration, what changes is the magnitude of the velocity.

2. Normal acceleration, does not change the magnitude of the velocity, only changes the direction of the velocity.

3. Tangential acceleration is the acceleration along the tangent direction of the track when the particle moves in a curve. The normal acceleration is the acceleration along the normal direction of the track when the particle moves in a curvilinear motion.

When the object is not subject to external force, it is in a state of uniform linear motion or stationary state, so when the object is moving curvially, it must be affected by the external force, so the acceleration is not zero, that is, the object must have acceleration when moving in a curve.

The direction of acceleration is not in the same straight line as the direction of velocity, and the object moves in a curve.

There are two main curvilinear movements in high school:

Flat throwing motion: Acceleration is the acceleration of gravity, and the direction is always vertical downward and uniform circular motion: the direction of acceleration is always perpendicular to the direction of velocity and points to the center of the circle.