10:21 AM Thu Mar 2 T d AL d M₁ ¡M₂ Before Collision P M₂ After Collision O+ TOP VIEWS 12.A system consists of a ball of mass M2 and a uniform rod of mass M₁ and a length d. The rod is attached to a horizontal frictionless table by a pivot at point P and initially rotates at an angular speed w, as shown above left. The rotational inertia of the rod about point P is M₁d². The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves in the direction shown above right. Express all answers in terms of M₁, M2, w, d, and fundamental constants. a. Derive an expression for the angular momentum of the rod about point P before the collision. b. Derive an expression for the speed v of the ball after the collision. 84% +: c. Assuming this collision is elastic, calculate the numerical value of the ratio of M₁/M2. -12 10:22 AM Thu Mar 2 T X 0)+ 84% +: Before Collision d. A new ball with the same mass M₁ as the rod is now placed a distance x from the pivot, as shown above. Again assuming the collision is elastic, for what value of x will the rod stop moving after hitting the ball? {Hint: Find the velocity of the ball after the collision first} < / 3 <
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
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