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In mathematics, a tangent to a path refers to a line that touches the path at a single point without crossing through it. It represents the instantaneous direction of motion at that point on the path. Tangents are often used in calculus to calculate rates of change or slopes of curves at specific points. In physics, tangents to the path of a moving object can represent its velocity or acceleration at a given moment.

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3w ago
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10y ago

The immediate surroundings of any point on a curved path can be considered as part of a circle: the circle of curvature at that point. Then the tangent to the path at that point is a line that meets the path at only one point in that neighbourhood and which is perpendicular to the line joining the point to the centre of the circle or curvature.

The concept can be extended to straight segments of the path by assuming that the centre of curvature is at an infinite distance. In that case, the path and its tangent are the same line.

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12y ago

The tangent to a curve at a point refers to the straight line that best approaches the curve. In other words, in a small interval the straight line it will go in the same direction as the curve.

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Q: What is meant by 'tangent to the path?
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Why acceleration is tangent to the path?

Acceleration is tangent to the path because it is a measure of the rate of change of velocity. By being tangent to the path, acceleration describes how the direction or speed of an object is changing as it moves along a curved path. The tangential component of acceleration is responsible for changes in speed, while the normal component of acceleration is responsible for changes in direction.


What is meant by tangential speed?

Tangential speed refers to the speed of an object as it moves along a curved path. It is the speed of an object in the direction tangent to the curve at any given point. This speed is perpendicular to the centripetal force that keeps the object moving in a circular path.


When is the velocity vector of a particle tangent to the path of the particle?

The velocity vector of a particle is tangent to the path of the particle at any point. This is because velocity is a vector that points in the direction of motion of the particle at that particular instant.


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What is meant by centripetal acceleration is perpendicular to velocity?

Centripetal acceleration is the acceleration directed towards the center of the circular path of an object in motion. When centripetal acceleration is perpendicular to velocity, it means that the acceleration is acting in a direction that is perpendicular to the direction of the object's motion at any given point along the circular path.


Why is velocity tangential to the path of a body?

Velocity is a vector; having direction. So, when changing direction constatly to have velocity a tangent can be drawn to the constantly changing path of the object having velocity.


What is meant by tangent to a curve at a point?

It is a straight line that touches the curve such that the line is perpendicular to the radius of the curve at the point of contact.


What is the direction of an object moving along a circular path?

The direction of an object moving along a circular path is constantly changing. At any given point, the direction of the object is tangent to the circle at that point.


Why the velocity and acceleration of body moving with uniform speed in circular path will be mutually perpendicular?

The velocity of an object moving in a circular path is always tangent to the circle at that point. Meanwhile, the acceleration of the object is directed towards the center of the circle, called centripetal acceleration. Since the velocity is tangent to the circle and the acceleration is pointing towards the center, they will be mutually perpendicular.


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A common tangent is a line which is tangent to two (or more) curves.


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