How is the acceleration of an object in uniform circular motion constant?
A) In magnitude only
B) In direction only
C) Both in magnitude and direction
D) In magnitude, direction and orientation

Question

How is the acceleration of an object in uniform circular motion constant? 
 A) In magnitude only 
B) In direction only
C) Both in magnitude and direction
D) In magnitude, direction and orientation

anonymous · Answer

If an object is in uniform circular motion, we know two things: 
First, the object's angular velocity is constant. 
Second, the radius of the circular path the object is following remains constant. 

We know intuitively that for an object to follow a circular path, it must have an acceleration component directed towards the center of rotation. |dw:1384399152644:dw|This acceleration is known as centripetal acceleration. We can quantify this centripetal acceleration with the following equation: $$a_c = {v^2 \over r}$$where v is the linear velocity, as shown|dw:1384399283305:dw|

So, if we know that v is constant, then centripetal acceleration must be constant in magnitude. But as we move around the circumference, we can observe that the direction of the centripetal acceleration must change such that it is always directed towards the center of the circle.