Q10DQ - University Physics with Modern Physics

Question

In uniform circular motion, what are the average velocity and average acceleration for one revolution? Explain. 

Step-by-Step Solution

Answer

The average velocity an object in circular motion is zero and the average acceleration of an object in circular motion is $\frac{v^2}{r}$.

Step 1: Concept/Significance of circular motion.

Circular motion is a two-dimensional motion of an item along a circular route in which the distance between two reference points in the plane is constant at all times.

Step 2: Determination of the average velocity for one revolution.

The rate of change of velocity is defined as average velocity. It's a quantity with a vector. An object in circular motion moves at a constant speed but not at a constant velocity. Because velocity has both magnitude and direction, but in circular motion, there will be just magnitude and no direction because the motion of the item changes direction at every point along the circular route, but it has magnitude. Speed is a scalar number with simply a magnitude and no direction. As a result, an item travels at a constant average speed.

 

Thus, an object travelling on a circular motion has zero average velocity.

Step 3: Determination of the average acceleration for one revolution.

The tangential acceleration of a circular motion object is 0 since the item is moving at a constant speed. For an item travelling in a circular route, however, centripetal acceleration exists. The centripetal acceleration of an item allows it to travel in circles. The centripetal force pulls the item toward the circle's centre due to centripetal acceleration. This is the average acceleration alone. the average acceleration is given by,

$a_{av}=\frac{v^2}{r}$

Here, v is the velocity of the object and r is the radius of circular orbit.

 

Thus, the average acceleration of an object in circular motion is $\frac{v^2}{r}$.