A solid, horizontal cylinder of mass 13.4 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system. rad/s=
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.
A solid, horizontal cylinder of mass 13.4 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.
rad/s=
Given: The mass of horizontal cylinder is 13.4 kg.
The radius is 1.00 m.
The angular speed of cylinder is 7.50 rad/s.
The mass of the putty is 0.250 kg.
The distance between the putty and the cylinder is 0.900 m.
To determine: The final angular speed of the system.
The angular momentum of the system is conserved, that is the initial angular momentum is equal to final angular momentum of the system.
The formula to calculate initial angular momentum is
....................... (1)
where I is the momentum of inertia of the cylinder and w is the angular frequency.
The formula to calculate the moment of inertia is
Substitute for I in equation (1)
Substitute 13.4 kg for m, 1.00 m for r and 7.50 rad/s for w in the above equation,
The final angular momentum is
where is
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