Graphing Circular Motion Concepts

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Questions and Answers

What is the trajectory graph for uniform circular motion?

A circle

What is any motion in which an object repeats the same movement over and over called?

Oscillatory motion

Flashcards

Oscillatory Motion

Any motion in which an object repeats the same movement over and over. It can be described mathematically using sine or cosine waves, which show smooth periodic oscillation.

Trajectory

The path a projectile takes through the air. It's a curved path shaped like a parabola. It can be represented mathematically using a quadratic function.

Trajectory Graph

A two-dimensional dot diagram that shows the object's total trajectory, which can be drawn as a line or a two-dimensional dot diagram.

Position Graph

A graph that displays the position of an object over time. This graph can help determine information such as an objects average and instantaneous velocity.

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Velocity Graph

A graph showing the velocity of an object over time. It can be used to deduce acceleration and displacement.

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Uniform Motion

Motion with a constant velocity. The horizontal motion of a projectile is an example.

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Accelerated Motion

Motion with constant acceleration. The vertical motion of a projectile is an example. The acceleration is due to gravity.

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Centripetal Acceleration

The acceleration of an object in uniform circular motion. It is always directed towards the center of the circle. The magnitude of the acceleration is constant, but its direction changes.

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Centripetal Vector

Describes a two-dimensional vector quantity (like velocity) that is always directed towards the center of a circle.

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Similar Triangles

The ratio of the corresponding sides of similar triangles are equal. The ratio of one side of a triangle to its counterpart in a similar triangle is constant for all sides.

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Adding Velocities in Two Dimensions

The sum of the x-components of the velocities to get the x-component of the resulting velocity. Then, add the y-components of the velocities to get the y-component of the resulting velocity. Finally, use the Pythagorean theorem to determine the magnitude of the resultant velocity, using the calculated x and y components.

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Projectile

An object moving through the air, only affected by gravity. It is the combination of uniform horizontal motion and free-fall motion.

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Projectile Motion

The combination of uniform motion parallel to Earth's surface combined with free-fall motion with constant acceleration perpendicular to Earth's surface.

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Analyzing Projectile Motion

The motion of a projectile can be analyzed by separating the motion into two independent one-dimensional motions, along the horizontal and vertical axes.

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Velocity

The rate of change of displacement, or how fast an object is moving in a specific direction, and can be represented mathematically as a set of vector components.

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Velocity Components of Projectile

The horizontal component of velocity of a projectile remains constant while the vertical velocity component changes.

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Acceleration

The rate of change of velocity over time, and can be represented mathematically as a set of vector components.

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Acceleration Due to Gravity

The acceleration due to gravity is constant and always acts downward towards the center of Earth.

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Uniform Circular Motion

Motion with a constant velocity in a circular path. Although the speed of the object remains the same, its direction is constantly changing, resulting in acceleration.

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Resultant Velocity

The resultant velocity of an object is the vector sum of its horizontal and vertical velocity components. It can be used to find the object's speed and direction.

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River Crossing

A river current pushes a boat downstream with a certain velocity. When the boat is rowed across the river, the two velocities (the boat's and the river's) add to produce a resultant velocity that is a combination of both.

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River Crossing Example

A person rows a boat across a river with a constant velocity. The river current pushes the boat downstream with a different constant velocity.

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Magnitude of Velocity

The magnitude of a velocity vector can be found using the Pythagorean theorem, given its x and y components.

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Direction of Velocity

The components of a velocity vector can be used to determine its direction relative to a coordinate system.

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Period

The time it takes for an object to complete one cycle of oscillatory motion.

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Frequency

The number of oscillations an object completes in a given amount of time.

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Study Notes

Graphing Circular Motion

  • The trajectory graph for uniform circular motion is a circle.
  • However, the graphs of position vs. time for the horizontal and vertical motions appear to oscillate.
  • An oscillatory motion is any motion in which an object repeats the same movement over and over.
  • Oscillatory motion can be described mathematically using either a sine wave or a cosine wave.
  • These are trigonometric curves that describe smooth periodic oscillation.
  • When a sine wave is at its maximum, the corresponding cosine wave is at its zero, and vice versa.
  • The equations for oscillatory motion are: x = R cos(ωt/R) and y = R sin(ωt/R)

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