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.
![Part E
Find the ring's angular speed when it is in the second orientation.
Express your answer in radians per second.
• View Available Hint(s)
ΑΣφ
?
W =
rad/s
Submit](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcffe6fb8-a8b1-4738-951c-b41ccaeecf4e%2Fb970f4e6-b453-4b36-8fa8-41956d7f0f33%2F7fy69p9_processed.png&w=3840&q=75)
![Part B
A circular ring with area 4.45 cm² is carrying a current of 13.5 A.
The ring, initially at rest, is immersed in a region of uniform
magnetic field given by
B = (1.35 x 10-2 T)(12i +3j – 4k). The ring is positioned
initially such that its magnetic moment orientation is given by
i; = µ(-0.8i + 0.6j), where µ is the (positive) magnitude of
the magnetic moment.
Determine the components of initial magnetic torque of the current-carrying ring.
Express your answers in newton-meters separated by commas.
• View Available Hint(s)
(a) Find the initial magnetic torque on the ring.
?
(b) The ring (which is free to rotate around one diameter) is
released and turns through an angle of 90.0° , at which point its
magnetic moment orientation is given by u = -µk. Determine
the decrease in potential energy.
Tx, Ty, Tz =
N.m
(c) If the moment of inertia of the ring about a diameter
is 2.50 x 10-7 kg · m² , determine the angular speed of the ring
as it passes through the second position.
Submit
Part C
Find the change in potential energy from the first orientation of the ring to the second orientation.
Express your answer with the appropriate units.
• View Available Hint(s)
HẢ
?
AU =
Value
Units
Submit
Part D
Find the rotational kinetic energy of the ring when it is in the second orientation.
Express your answer with the appropriate units.
View Available Hint(s)
HÅ
Value
Units
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcffe6fb8-a8b1-4738-951c-b41ccaeecf4e%2Fb970f4e6-b453-4b36-8fa8-41956d7f0f33%2Ffrgxie_processed.png&w=3840&q=75)
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