A rod of mass M and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving with speed V, strikes the rod at angle θ from the normal and sticks to the rod after the collision.What is the angular speed ωf of the system immediately after the collision, in terms of system parameters and I? Use the conservation of angular momentum. To find the initial angular velocity of the system, you will have to find the initial angular velocity of mass - which is related to the linear velocity of the ball perpendicular to the rod. The image illustrates a physical scenario involving a collision between a moving object and a rod. Here is the detailed description of the diagram:- A horizontal rod of mass \( M \) is shown, pivoted at one end (left side), allowing it to rotate about that point.- The rod has a total length \( L \).- A red ball with mass \( m \) is moving towards the rod. - The ball's velocity is indicated by \( V \), and it approaches the rod at an angle \( \theta \) with respect to the perpendicular line from the point of collision to the pivot.- \( D \) represents the distance from the pivot to the point where the ball collides with the rod.This setup is likely used to analyze the conservation of momentum and angular momentum, as well as to study the dynamics of rotational motion.

Given: Mass of the putty ball, mp=mMass of the rod, mr=MVelocity of the ball, vb=vLength of the rod, Lr=L Apply the conservation of the angular momentum. Initial angular momentum is equal to the final angular momentum. Li=Lf .... (1) Initial angular momentum: mvcosθD Final angular momentum: Lf=ML23+mD2ωf Substitute the value in equation (1). mvcosθD=ML23+mD2ωfωf=mvcosθDML23+mD2 The angular speed ωf of the system immediately after the collision is mvcosθDML23+mD2.

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Advanced Physics

A rod of mass M and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving with speed V, strikes the rod at angle θ from the normal and sticks to the rod after the collision. What is the angular speed ωf of the system immediately after the collision, in terms of system parameters and I?

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