Fundamental doubt on Acceleration.

[PhysicsBegner]

Hi Everyone, I have very fundamental question on Acceleration. I can understand that a moving body accelerates or de-accelerate when its velocity goes up and down.

But I couldn't understand; when we say a moving body accelrates or de-accelerates when the direction of moving body changes(with constant velocity). What acceleration literally means here?

I can understand mathematically since velocity is a vector we get acceleration whenever magnitude or direction changes. But I couldn't understand logically what acceleration means here.

 

[Vagn]

Hi Everyone, I have very fundamental question on Acceleration. I can understand that a moving body accelerates or de-accelerate when its velocity goes up and down.

But I couldn't understand; when we say a moving body accelrates or de-accelerates when the direction of moving body changes(with constant velocity). What acceleration literally means here?

I can understand mathematically since velocity is a vector we get acceleration whenever magnitude or direction changes. But I couldn't understand logically what acceleration means here.

Whenever an object changes speed or direction then it feels a force and therefore acceleration, because velocity is a vector quantity. Acceleration in the case you have given, where it has constant speed, means that the force is perpendicular to the velocity of the body, which means it is moving in a circle.

 

[PhysicsBegner]

I think u misunderstood only force causes acceleration, No force then no acceleration(Newton's first law). My doubt was: if we calculate acceleration of a body moving with a constant velocity in a circle using centripetal force then wold it be equal to the acceleration calculated by direction change of velocity.

 

[Doc Al]

My doubt was: if we calculate acceleration of a body moving with a constant velocity in a circle using centripetal force then wold it be equal to the acceleration calculated by direction change of velocity.

Yes, of course. Those are just two ways of saying the same thing. (I assume you mean a body moving in a circle with constant speed, not constant velocity.)

You can calculate the acceleration of the object as kinematic exercise, getting a_c = v^2/r. Applying Newton's 2nd law gives you F_c = ma_c. It's the same acceleration either way.

 

[HallsofIvy]

I think u misunderstood only force causes acceleration, No force then no acceleration(Newton's first law). My doubt was: if we calculate acceleration of a body moving with a constant velocity in a circle

As Doc Al implies, this is impossible. To move with a constant velocity means to move at a constant speed in a straight line. "Velocity" is a vector quantity having both magnitude and direction. Change in either magnitude (speed) or direction is an acceleration.

using centripetal force then wold it be equal to the acceleration calculated by direction change of velocity.

You are confusing "velocity" and "speed".

 

[PhysicsBegner]

Yes, I meant constant speed not velocity. I was confused since some textbooks use term velocity instead of speed at certain places. And I understand that a body can't travel in circular path with constant velocity.

Thank you.