This Two-Dimensional motion unit covers projectile motion and circular motion, as well as the Newton's law of Universal Gravitation.
PROJECTILE MOTION:
Objects are projectiles when the only force acting on them is gravity. As projectiles move through the air, their motion is split into an X component and a Y component. Projectiles move in a constant velocity in the X direction and accelerate downward (at 9.8 m/s/s here on Earth) in the Y Direction. These two components can be modeled using kinematic equations.
PROJECTILE MOTION:
Objects are projectiles when the only force acting on them is gravity. As projectiles move through the air, their motion is split into an X component and a Y component. Projectiles move in a constant velocity in the X direction and accelerate downward (at 9.8 m/s/s here on Earth) in the Y Direction. These two components can be modeled using kinematic equations.
https://www.youtube.com/watch?v=ZZ39o1rAZWY
CIRCULAR MOTION:
Circular describes the forces of an object moving around a circular path. The rate at which an object spins is its angular velocity, and is usually measured in radians per second, or ω. To find the speed of an object from it's angular velocity, multiply its angular velocity in radians per second by the object's distance from the center of the circle, in meters. While these objects may have a constant speed, their velocity is constantly changing. Looking at the change in velocity of an object over a small distance around the circle, it becomes apparent that the direction of the change in velocity, and therefore the acceleration, points toward the center of the circular path:
Circular describes the forces of an object moving around a circular path. The rate at which an object spins is its angular velocity, and is usually measured in radians per second, or ω. To find the speed of an object from it's angular velocity, multiply its angular velocity in radians per second by the object's distance from the center of the circle, in meters. While these objects may have a constant speed, their velocity is constantly changing. Looking at the change in velocity of an object over a small distance around the circle, it becomes apparent that the direction of the change in velocity, and therefore the acceleration, points toward the center of the circular path:
The magnitude of this acceleration, centripetal acceleration is modeled by the equation a=(v^2)/r, where v is the object's speed or instantaneous velocity, and r is the radius of the circular path. Combining this with Newton's 2nd law, F=ma, the equation for the net force of an object in circular motion, the centripetal force, is F=m(v^2)/r, where m is the mass of the object.
Click the image to download a 2D motion simulator. You may need to go into your computer's settings to allow the simulation to run. Drag the red dot in a circle and note the direction and magnitude of the velocity and acceleration vector arrows.
Credit: https://phet.colorado.edu/en/simulation/legacy/motion-2d |
NEWTON'S LAW OF UNIVERSAL GRAVITATION:
Newton's Law of Universal Gravitation describes the force of gravity between two objects using their masses and the distance between their centers of mass. The law states that the gravitational force between two objects is G(m1)*(m2)/r^2, where m1 and m2 are the masses of the two objects and r is the distance between their centers of mass. G, not to be confused with g, the acceleration due to gravity on earth, is a constant with the value 6.67*10^-11.
Newton's Law of Universal Gravitation describes the force of gravity between two objects using their masses and the distance between their centers of mass. The law states that the gravitational force between two objects is G(m1)*(m2)/r^2, where m1 and m2 are the masses of the two objects and r is the distance between their centers of mass. G, not to be confused with g, the acceleration due to gravity on earth, is a constant with the value 6.67*10^-11.
https://www.youtube.com/watch?v=7gf6YpdvtE0
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