Change in direction and acceleration

[quantizedzeus]

Why and how does Change in direction of a moving body accelerate it?

 

[Doc Al]

Why and how does Change in direction of a moving body accelerate it?

What's the definition of acceleration?

 

[kiwakwok]

Displacement, velocity and acceleration are vector quantities. A vector quantity not only consists of magnitude (a real number/scalar) but it also consists of direction.

Recall that the definition of acceleration is time rate of change of velocity vector. We care both the magnitude and direction.

You may have a look on the topic of uniform circular motion.

 

[sankalpmittal]

Why and how does Change in direction of a moving body accelerate it?

It may be mentioned that while the velocity also determines the direction of body , acceleration does not determine the direction of body . Acceleration is a vector quantity because it can be negative . This is because a body can accelerate or retard . Positive and negative sign in acceleration just tell that whether speed is increasing (velocity for particular) or decreasing . For eg. -5m/s² tell that a body retards by 5m/s velocity .
Change in direction does not bring acceleration . Change in direction means variable velocity and variable velocity means change in velocity per unit time .
Here variable velocity is bringing acceleration . Change in direction is cause of variable velocity.

http://en.wikipedia.org/wiki/Uniform_circular_motion"

Orhttp://www.physicsclassroom.com/mmedia/circmot/ucm.cfm"

Also see scalar and vector quantities.

Vector quantity : Direction + Magnitude and; +ve and -ve. Eg. Displacement , acceleration , velocity etc .

Scalar quantity :Only Magnitude ;and only +ve . Eg. Distance , speed , mass etc .

 

[Philip Wood]

Sankalpmittal is not using the term 'acceleration' as physicists use it.

Acceleration is defined as rate of change of velocity. When a body changes its direction it changes its velocity, so it has an acceleration This is not just playing with words: we can even calculate the magnitude of a body's acceleration when it goes in a circle at constant speed.

Strictly, acceleration cannot be positive or negative. It is a vector quantity and has magnitude and direction. Informally, we may talk of accelerations being positive or negative, but we're really talking about the component of acceleration in a chosen direction. The same remark applies to velocities and displacements, indeed to all vectors.

 

[Philip Wood]

Quantizedzeus... To go a step further, do you know how to subtract vectors? It's the essential skill needed in order to find the acceleration when a body changes direction. You consider a time interval \deltat. You find the change in velocity \deltav during \deltat thus:
\deltav = v_final - v_initial.
The subtraction is, of course, a vector subtraction.
You then divide \deltav by \deltat to get the mean acceleration during \deltat. Finally you find the limit to which this converges as \deltat approaches zero, to get the instantaneous acceleration.

The simplest example, and by far the most important case, is a body moving in a circle at constant speed. It is dealt with in almost any standard mechanics text.