Lecture on Translational and Rotational Motion Post-Collision

Date: July 10, 2024

Problem Statement

A thin rod of mass M and length L rests on a frictionless table. It is struck at a point L/4 from its center of mass by a clay ball of mass m, moving with speed v. Upon collision, the clay ball sticks to the rod.

Questions to Determine:

1. Translational motion of the rod after the collision.
2. Rotational motion of the rod after the collision.

Initial Conditions and Setup

• Rod: Mass = M, Length = L
• Clay Ball: Mass = m, Speed = v
• Collision Point: L/4 from the rod's center of mass
• After collision, the clay ball sticks to the rod

Key Points:

• Translational Motion: This involves the movement of the rod's center of mass post-collision.
• Rotational Motion: This involves the rod rotating about its center of mass post-collision.

Analysis

Translational Motion

• Conservation of Linear Momentum: The total linear momentum before and after the collision must be conserved because there are no external forces acting on the system.

Rotational Motion

• Conservation of Angular Momentum: The total angular momentum should be conserved about the center of mass.

Difficulty Levels

• Varies depending on your background in physics. For college physics students, this problem is manageable.
• Similar types of problems might have been covered in physics courses, such as MIT's courses 801 or 803.

Recommendations

• Spend some time solving the problem, especially if this topic is new to you.

Conclusion

• Practice and understanding of these fundamental physics principles are crucial for mastering such problems.

Have a great July 10!