a small object is placed in a groove in a rotating disc. we know it moves in radially outward direction.but if we observe motion of object in an inertial frame(so we can't assume centrifugal force), which force is responsible for its motion in radially outward direction and which force is providing it centripetal force?

When a small object is placed in a groove on a rotating disc, it indeed moves in a radially outward direction. To understand the forces at play in an inertial frame, we need to analyze the situation carefully. In this context, the object experiences two main forces: the centripetal force that keeps it moving in a circular path and the force that causes it to move outward.

Understanding the Forces Involved

In an inertial frame, we don't consider fictitious forces like centrifugal force. Instead, we focus on the actual forces acting on the object. Here’s how it works:

Centripetal Force

The centripetal force is essential for any object moving in a circular path. It acts towards the center of the circular path. In this case, the force providing the centripetal acceleration is the frictional force between the object and the groove of the disc. This frictional force prevents the object from sliding off as the disc rotates.

Radial Outward Motion

The outward motion of the object can be attributed to its inertia. When the disc starts to rotate, the object tends to maintain its state of motion due to inertia, which is the tendency of an object to resist changes in its state of motion. As the disc rotates, the object moves outward because it is trying to maintain its straight-line path, which is a consequence of Newton's first law of motion.

Breaking It Down with an Example

Imagine you are sitting in a car that suddenly takes a sharp turn. Your body tends to lean outward, away from the center of the turn. This is similar to what happens with the object on the rotating disc. As the disc spins, the object feels a tendency to move straight outwards due to inertia, while the frictional force acts inward to keep it in circular motion.

• Centripetal Force: Provided by friction, directed towards the center of the disc.
• Inertial Outward Motion: The object's tendency to move straight due to inertia.

Conclusion on Forces

In summary, in an inertial frame, the centripetal force that keeps the object in circular motion is the frictional force acting towards the center of the disc. The outward motion is a result of the object's inertia, which tries to maintain its straight-line path. Understanding these forces helps clarify the dynamics of objects in rotational motion without relying on fictitious forces.