Why uniform circular motion is said to be accelerated ?

Question

Answer

Uniform Circular Motion: Accelerated Motion

In uniform circular motion, an object moves in a circular path at a constant speed. Although the speed is constant, the object is still considered to be undergoing accelerated motion. This may seem contradictory at first, as acceleration is often associated with a change in speed. However, in the case of uniform circular motion, acceleration refers to the change in the object's direction rather than its speed.

Centripetal Acceleration

In circular motion, there is a force called the centripetal force that acts towards the center of the circle, keeping the object on its circular path. This force is responsible for continuously changing the object's direction, and it is always perpendicular to the velocity vector at any given point.

The centripetal force causes the object to experience centripetal acceleration, which is defined as the rate of change of velocity in the direction of the center of the circle. This acceleration is always directed towards the center of the circle and is perpendicular to the object's velocity vector.

Acceleration and Velocity Vectors

In order to understand why uniform circular motion is considered accelerated, it's important to consider the relationship between acceleration and velocity vectors. Acceleration is a vector quantity, meaning it has both magnitude and direction. In circular motion, the acceleration vector is constantly changing its direction, even if the magnitude remains constant.

The velocity vector represents the object's speed and direction of motion. As the acceleration vector constantly changes its direction, it causes a continuous change in the direction of the velocity vector. This change in direction indicates a change in velocity, even if the speed remains constant. Thus, the object is considered to be undergoing accelerated motion.

Mathematical Representation

Mathematically, the magnitude of the centripetal acceleration can be determined using the following formula:

ac = v^2 / r

Where ac represents the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path. This formula shows that centripetal acceleration is inversely proportional to the radius of the circle, meaning that a smaller radius will result in a larger acceleration.

Conclusion

Uniform circular motion is considered to be accelerated because the object undergoes a continuous change in direction, even if its speed remains constant. The centripetal acceleration, caused by the centripetal force acting towards the center of the circle, is responsible for this change in direction. While the object's speed remains the same, its velocity vector constantly changes, indicating accelerated motion.

Answer

Can I write like this ' it is said to be accelerated because it have a constant velocity '

Answer

In uniform circular motion, the direction of motion of the object keeps changing. Velocity changes with change in direction as it is vector and change in velocity means acceleration. Therefore uniform circular motion is accelerated motion.

Answer

Because it has a change in velocity.

Answer

Because it change its direction. speed with direction is known as velocity and further change in velocity means acceleration

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