## Table of Contents

By following these steps, you can methodically solve circular motion problems with a deeper understanding of the physical principles involved. This approach not only aids in finding numerical solutions but also in grasping the conceptual framework underlying circular motion dynamics.

## Step 1: Draw a Comprehensive Free Body Diagram (FBD)

Begin by sketching a detailed Free Body Diagram that includes all the forces acting upon the object in motion. It’s crucial to accurately represent the magnitude and direction of each force. Remember, the centripetal force, which is essential in circular motion, is not an additional force but rather the net result of the forces acting towards the center of the path. Hence, include it in your diagram only if specifically required, or to illustrate the net force causing the object to move in a circular path.

## Step 2: Identify the Center of the Circular Path

Clearly determine and mark the center of the circular path around which the object is moving. Understanding the geometric center of the path is vital as it helps in accurately resolving forces and understanding the motion’s dynamics.

## Step 3: Resolve Forces Along Two Axes

Break down the forces into components along two mutually perpendicular axes:

**Radial Axis (towards the center of the circle):**Resolve forces in the direction pointing towards the center of the circular path. These components contribute to the centripetal force necessary for circular motion.**Tangential Axis (perpendicular to the radial direction):**Resolve forces in the direction tangential to the circle. These components are responsible for any tangential acceleration, affecting the speed of the object without influencing its circular path.

## Step 4: Formulate the Net Force Expression

Write down the mathematical expression for the net force directed towards the center of the circular path. This net inward force is what causes the centripetal acceleration ($a_c$) of the object in circular motion. The centripetal force ($F_c$) can be expressed as $F_c = m \cdot a_c$, where $m$ is the mass of the object and $a_c$ is the centripetal acceleration.

## Step 5: Apply Newton’s Second Law Along Each Axis

Utilize Newton’s Second Law ($F = ma$) to relate the forces acting on the object to its motion along each axis:

**Radial Axis:**Apply Newton’s Second Law to find the centripetal force needed for circular motion. This involves equating the net radial force to the product of the mass of the object and its centripetal acceleration ($F_{\text{net, radial}} = m \cdot a_c$).**Tangential Axis:**If there is tangential acceleration, apply Newton’s Second Law to determine the net tangential force and its effect on the object’s speed. This involves equating the net tangential force to the product of the mass of the object and its tangential acceleration ($F_{\text{net, tangential}} = m \cdot a_t$).