(c) What is the total kinetic energy of this system? Ktot 6431.5 (d) What is the translational kinetic energy of this system? Ktrans = X J (e) What is the kinetic energy of this system relative to the center of mass? Krel=
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.
![Consider a system consisting of three particles:
m₁ = 3 kg,
₁ = < 7, -8, 14 > m/s
m₂ = 6 kg,
2 = < -15, 7, -4> m/s
m3 = 4 kg, 3 = < -23, 38, 24 > m/s
(a) What is the total momentum of this system?
-161,170,114)
kg. m/s
P tot
=
(b) What is the velocity of the center of mass of this system?
cm = (-12.38,13.08,8.77)
m/s
(c) What is the total kinetic energy of this system?
Ktot = 6431.5
J
(d) What is the translational kinetic energy of this system?
Ktrans =
X J
(e) What is the kinetic energy of this system relative to the center of mass?
Krel =
J
One way to calculate Krel is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the particle's
velocity relative to the center of mass, then calculating the corresponding kinetic energy, then adding up the three relative kinetic energies. However, there is a much simpler way to determine the
specified quantity, without having to do all those calculations; think about what you know about the relationships among the various kinds of kinetic energy in a multiparticle system. (If you wish,
you can check your result by doing the complicated calculation just described.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c83a6cc-70d7-4a20-8726-e601d846e6ec%2F3ebc68af-b16b-46ba-8d73-ce450570367b%2F7hg4up_processed.png&w=3840&q=75)
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