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.
![Find A.
A 0.567 m/s
A disk of radius 24.0 cm is free to turn about an axle perpendicular to it through
its center. It has very thin but strong string wrapped around its rim, and the string
is attached to a ball that is pulled tangentially away from the rim of the disk (the
figure (Figure 1)). The pull increases in magnitude and produces an acceleration
of the ball that obeys the equation a (t)= At, where t is in seconds and A is a
constant. The cylinder starts from rest, and at the end of the third second, the
ball's acceleration is 1.70 m/s .
%3D
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v Correct
Part B
Express the angular acceleration of the disk as a function of time.
?
a(t) =
– 4.166
(rad/s*)t
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X Incorrect; Try Again; 3 attempts remaining
Part C
How much time after the disk has begun to turn does it reach an angular speed of 12.5 rad/s?
t = 3.25 s
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v Correct
Figure
1 0.1 >
Part D
Through what angle has the disk turned just as it reaches 12.5 rad/s ? (Hint: See Section 2.6 in the textbook.)
Ball
0-00 = 13.6 rad
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Disk
v Correct
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