We will assume that the velocity of Juan's hand and the pencil were both 3.6 meters per second prior to impact and that his wrist added an angular velocity to the pencil of 3.4 radians/second. In reality the pencil dug in nearest to my thumb and did not poke through the back. For the purpose of this calculation we will instead say that the blue pencil of mass M and length of L pushed through my hand until 23% of its length was behind the hand. We will further assume that the normal force between the hand and the pencil was 80 Newtons and that the area of the point of the pencil was 0.0015 mm2. The coefficient of kinetic friction between the pencil exterior and my flesh was 0.35 because I was running a slight fever and had a temperature of 101 degrees Fahrenheit. Write an expression for dm: dm =
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.
We will assume that the velocity of Juan's hand and the pencil were both 3.6 meters per second prior to impact and that his wrist added an
Write an expression for dm: dm =
Write the result for the Moment of Inertia: I =
The formula for Moment of Inertia in the form of an integral: I = ∫
Write an expression for the upper limit of the integral: Upper Limit =
Write an expression for r: r =
Write an expression for the lower limit of the integral: Lower Limit =
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