a body has pure rotation. the particle of the body at the lower most position has instantaneous acceleration. true or false? give reason.

In the scenario where a body is undergoing pure rotation, the statement that a particle at the lowest position has instantaneous acceleration is true. Let’s break this down to understand why.

Understanding Pure Rotation

Pure rotation refers to the motion of an object rotating around a fixed axis without any translational movement. In this case, every point on the body moves in a circular path around the axis of rotation.

Acceleration in Rotational Motion

When we talk about acceleration in the context of rotational motion, we need to consider two components:

• Tangential Acceleration: This occurs if there is a change in the speed of rotation. In pure rotation at constant angular velocity, this component is zero.
• Centripetal Acceleration: This is always present in circular motion, directed towards the center of the circle. It is given by the formula a_c = ω²r, where ω is the angular velocity and r is the radius.

Instantaneous Acceleration at the Lowest Position

Now, let’s focus on the particle at the lowest position of the rotating body. Even if the body is rotating at a constant speed, this particle experiences centripetal acceleration directed towards the center of the rotation. Therefore, it does indeed have instantaneous acceleration at that point.

Example for Clarity

Imagine a Ferris wheel. As it rotates, each seat (or particle) moves in a circular path. When a seat is at the bottom, it is still accelerating towards the center of the wheel due to centripetal acceleration, even if it is not speeding up or slowing down. This is a clear demonstration of how a particle can have instantaneous acceleration while being in pure rotational motion.

Final Thoughts

In summary, the statement is true: a particle at the lowest position of a body in pure rotation does have instantaneous acceleration due to the centripetal force acting on it. This concept is fundamental in understanding the dynamics of rotating bodies and highlights the importance of distinguishing between different types of acceleration in rotational motion.