Chapter 5, Problem 1RQ

Review Question 5.1 How do we know that the sum of the forces exerted on an object moving in a circle at constant speed points toward the center of the circle?

To determine

The validity of the statement that the sum of the forces exerted on a body in circular motion, moving with constant speed, acts toward the center of the circle.

Answer to Problem 1RQ

Solution:

Using the Newton’s second law of motion it can be validated that there is force along radial direction only.

Explanation of Solution

Given data:

The body is undergoing circular motion at a constant speed.

Formula used:

Write the expression for Newton’s second law of motion.

$F_{net}=ma$

Here, $F_{net}$ is the net force acting on the body, $m$ is the mass and $a$ is the acceleration in the direction of net force.

Explanation:

For a body undergoing circular motion at a constant speed, the direction of motion changes at every instance of time. So the velocity, being a vector quantity, changes at every instant of time.

Also, the change in velocity in a circular motion gives rise to a radial acceleration. The direction of this radial acceleration is towards the center of the circle.

From Newton’s second law,

$F_{net}=ma$

The net force is the function of acceleration of the body of mass $m$ and the direction of force is in the direction of acceleration.

In case of uniform circular motion, the acceleration is the radial acceleration which acts in a direction towards the center of the circle. Hence, the net force acting in uniform circular motion with a constant speed also acts in the direction of the center of the circle.

Conclusion:

The net force acting on the body undergoing circular motion with a constant speed is a function of its acceleration which acts in a direction towards the center of circle of motion.