A point starts at the location (-5, 0) and moves CCW along a circle centered at (0, 0) at a constant angular speed of 2 radians per second. Let t represent the number of seconds since the point has swept out since it started moving. Draw a diagram of this to make sure you understand the context! a. Suppose the point has traveled for 0.1 seconds (t = 0.1). How many radians would need to be swept out from the 3-o'clock position [or from (5,0)] to get to the point's current position? b. Write an expression in terms of t to represent how many radians would need to be swept out from the 3-o'clock position to get to the point's current position. d. Sketch a graph of g. c. Write a function g that determine's the point's x-coordinate in terms t. g(t) = H -π -JU/2 8g(t) 6 radians Preview 4 2 -2 -4 -6 Preview J/2 -8- Clear All Draw: M Preview A 3/2 200
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.
![A point starts at the location ( – 5,0) and moves CCW along a circle centered at (0, 0) at a constant angular speed of 2 radians per second. Let t
represent the number of seconds since the point has swept out since it started moving. Draw a diagram of this to make sure you understand the
context!
a. Suppose the point has traveled for 0.1 seconds (t = 0.1). How many radians would need to be swept out from the 3-o'clock position [or from
(5, 0)] to get to the point's current position?
b. Write an expression in terms of t to represent how many radians would need to be swept out from the 3-o'clock position to get to the point's
current position.
d. Sketch a graph of g.
-π -J/2
radians
c. Write a function g that determine's the point's x-coordinate in terms t.
g(t) =
8 g(t)
6
4
2
J2
Preview
Preview
-2
-4
-6
-8+
Clear All Draw: M
П
Preview
3π/2
20t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a31831f-6f00-4468-acbe-9e4738be30a7%2F37c3d9ec-2d93-42c7-9457-014566ddf5d8%2Fyx04d2_processed.png&w=3840&q=75)
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