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 $\delta$t. You find the change in velocity $\delta$v during $\delta$t thus:
$\delta$v = v_final - v_initial.
The subtraction is, of course, a vector subtraction.
You then divide $\delta$v by $\delta$t to get the mean acceleration during $\delta$t. Finally you find the limit to which this converges as $\delta$t 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.