target and collides in a perfectly inelastic collision, which sets the target in motion around the pivot. The geometry of the masses are as follows: m4 = 1.27 kg is an aluminum disk of radius ra = 0.15 m which has a bearing at its center. This pivot point is shown as a dot in the figure. m3 = 0.150 kg is a uniform rod of length l = 1.0 m, and is attached to the ruler 20 cm from its end. mg = 0.5 kg is sitting on top of the ruler r = -0.15 m from the pivot, and Sm, (assume massless) is the target for the dart, located ra = 0.6 m from the pivot. The dart is shown as m = 0.10kg and collides directly with the center of the target (0.6 m from the pivot). a) Calculate the angular momentum of the system before the collision, assuming the dart is thrown at vii = 12 m/s. b) Calculate the moment of inertia of the rotating masses with the dart stuck into the target. c) Calculate the final angular velocity of the system after the collision.
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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