Podcast
Questions and Answers
What do R, θ, and z represent in polar coordinates?
What do R, θ, and z represent in polar coordinates?
What do eR, eθ, and ez represent in polar coordinates?
What do eR, eθ, and ez represent in polar coordinates?
What is the role of Coriolis acceleration in cylindrical coordinates?
What is the role of Coriolis acceleration in cylindrical coordinates?
Which type of acceleration does the term ⃗ contain in cylindrical coordinates?
Which type of acceleration does the term ⃗ contain in cylindrical coordinates?
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What aspect of motion does the derivative of unit vectors represent in polar coordinates?
What aspect of motion does the derivative of unit vectors represent in polar coordinates?
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At which point during its trajectory does a basketball reach its peak amplitude?
At which point during its trajectory does a basketball reach its peak amplitude?
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In what context would a basketball player need to calculate initial velocity and launch angle?
In what context would a basketball player need to calculate initial velocity and launch angle?
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What characteristic of a projectile's motion is significant when calculating initial velocity for a basketball shot?
What characteristic of a projectile's motion is significant when calculating initial velocity for a basketball shot?
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What is the primary purpose of using cylindrical coordinates in analyzing particle motion?
What is the primary purpose of using cylindrical coordinates in analyzing particle motion?
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What parameter does θ represent in polar coordinates?
What parameter does θ represent in polar coordinates?
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Study Notes
Coordinates
- Polar coordinates use the angle θ
- Cartesian coordinates use x-z, where z=L.cos θ and x=L.sin θ
Cause-and-Effect Principle
- If there is an effect, there must be a cause behind it
- In a well-defined problem, the cause's or effect's magnitude will not be known until the problem is solved
Dynamics
- Dynamics has two parts: kinematics and kinetics
- Kinematics is the study of the geometry of motion
- Kinetics deals with the forces imparted on bodies and the response (motion) of the bodies to these forces
Rigid Bodies
- A rigid body is a continuous distribution of particles, hence a particle system for which the relative distances and orientations of the constituent particles remain fixed
Kinematics of Particles
- A particle is a body that has mass but no volume
- Kinematics is the study of the geometry of motion
- To locate a particle, we must specify its location with respect to some reference by considering coordinate systems
Coordinate Systems
- There are many coordinate systems, including:
- Cartesian Coordinates
- Path Coordinates (normal & tangential)
- Cylindrical Polar Coordinates
Cartesian Coordinates
- Basis vectors are constant in direction and magnitude
- Position, velocity, and acceleration equations are simplified
- Figure 1-6 shows Cartesian coordinates
Path Coordinates (normal & tangential)
- Used to describe motion along a curved path
- Normal (n) and tangential (t) coordinates are used
- Figure 1-7 shows normal & tangential coordinates
- Velocity vector is always tangent to the motion path (t-direction)
- Acceleration has two components: change in magnitude and change in direction
Cylindrical Polar Coordinates
- Used when a particle moves along a 3-D curve
- Radial (R), angular (θ), and axial (z) coordinates are used
- Figure 1.36 shows cylindrical polar coordinates
- Instantaneous velocity is obtained by taking time derivatives of the position vector
- Derivative of unit vectors is necessary to derive acceleration
Example Problem
- A basketball player wants to shoot the basketball into the hoop
- The ball travels as a projectile and reaches a height of 5h=4 before it begins its descent towards the basket
- Calculate the initial velocity v0 and the player's angle to launch the ball
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Description
Test your knowledge on possible generalized coordinates like polar and cartesian coordinates, and concepts such as the Cause-and-Effect Principle. Explore dynamics, including kinematics and kinetics, with a focus on a simple model of a vehicle (tricycle model).
