Unit 3 is about circular motion. In this unit, we are going to explore Uniform Circular Motion, Angular Velocity, Centripetal Acceleration, Centripetal Force, and Universal Law of Gravitation. Also, we are going to see a lot of equations that will help us when we are doing questions. After students accomplish all the learning targets, and did the Space Station Project, they should understand the basic content of circular motion and be able to solve problems by using the equations.
Unit 3 Notes
Overview of the content in this unit:
Important Edpuzzle Notes:
- Qualitative dynamics of circular motion
- Analyzing velocity change for circular motion
- Radical acceleration and period
- Skills for analyzing processes involving circular motion
- The law of universal gravitation
Important Edpuzzle Notes:
Vertical Change Method to Find the Direction of Acceleration
- We can estimate the direction of an object's acceleration as it passes a point along its circular path by drawing an initial velocity vector Vi just before that point and a final velocity vector Vf just after the point. We place the vectors tail to tail and draw a velocity change vector from the tip of the initial to the tip of the final velocity. The acceleration points in the directions of the velocity change the vector.
Radical Acceleration for Constant Speed Circular Motion
- An object moving at constant speed along a circular path has acceleration that points toward the center of the circle and has a magnitude a(r) that depends on its speed v and the radius r of the circle.
Period and Radical Acceleration
- The radial acceleration can also be expressed using the period T of circular motion, the time interval needed for an object to complete one trip around the circle.
Sum of the Forces for Constant Speed Circular Motion
- The sum of the forces exerted on an object during constant speed circular motion points in the positive radial direction toward the center of the circle. The object's acceleration is the sum of the radial components of all forces exerted on an object divided by its mass -- consistent with Newton's second law. In addition, for horizontal circular motion, you sometimes analyze the vertical y-components of forces exerted on an object.
Law of Universal Gravitation
- This force law is used primarily to determine the magnitude of the force that the Sun exerts on planets or that planets exert on satellites or on moons. The force depends and on their center-to-center separation r.
Uniform Circular Motion
Circular Motion Variables
Circular Motion Equations
- Uniform Circular Motion - Motion in a circle at a constant speed
- Angular Velocity - Measure of how an angle changes over time. The rotational analogue of linear velocity. Vector quantity with counterclockwise defined as the positive direction.
- Centripetal acceleration - Acceleration pointed towards the center of a curved path and perpendicular to the object's velocity. Causes an object to change its direction and not its speed along a circular pathway.
- Period - Time needed for one revolution. Inversely proportional to frequency.
- Frequency - Number of revolutions per second for a rotating object.
Circular Motion Variables
- 𝚫𝜃 → angular displacement (in radians)
- ω → angular velocity (in rad/sec)
- 𝜶 → angular acceleration (in rad/sec/sec)
- T → period (in seconds)
- 𝑓 → frequency (in cycles/second or Hertz)
Circular Motion Equations
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
Angular Velocity and Tangential Speed
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Centripetal Acceleration & Centripetal Force
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Universal Law of Gravitation
- Newton’s universal law of gravitation: Every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is
- where F is the magnitude of the gravitational force. is the gravitational constant, given by
- Newton’s law of gravitation applies universally.
- More about the Universal Law of Gravitation
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