Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the angular acceleration when it has an angle of 10.0 degrees from the vertical? There are two reasonable approximations to consider for the pencil in this problem: a cylinder and a thin rod. However, in this problem we will treat the pencil as a uniform thin rod of length 15.0 cm and mass 10.0 g . Calculate the time ttt for the pencil to hit the ground, assuming that it falls from standing perfectly vertical and maintains this angular acceleration.
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.
Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the
There are two reasonable approximations to consider for the pencil in this problem: a cylinder and a thin rod. However, in this problem we will treat the pencil as a uniform thin rod of length 15.0 cm and mass 10.0 g .
Calculate the time ttt for the pencil to hit the ground, assuming that it falls from standing perfectly vertical and maintains this angular acceleration.
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