Unit 3 Overview
Not all motion is perfectly straight in one direction. Oftentimes, it has a curved path. According to Newton's First Law of Motion, an object will continue to move at a constant velocity unless it feels an unbalanced push or pull. Although the object is being rotated at a constant speed, the object is not moving at a constant tangential velocity, so an unbalanced force must be acting upon it that is in the same direction as the acceleration. Read on to find out!
This unit overview will cover two major topics -- Circular Motion and Universal Gravitational. Within that, we will delve into specific equations for each of these concepts, a visual representation along with the equations, and its relationship to real-life scenarios.
In this unit, we conducted the Circular Motion Lab, in which we swung an object with a constant radius at a constant speed to determine its acceleration.
This unit overview will cover two major topics -- Circular Motion and Universal Gravitational. Within that, we will delve into specific equations for each of these concepts, a visual representation along with the equations, and its relationship to real-life scenarios.
In this unit, we conducted the Circular Motion Lab, in which we swung an object with a constant radius at a constant speed to determine its acceleration.
Circular Motion
Coordinate Systems for Object in Circular Motion
Cartesian Coordinates (x,y)
Polar Coordinates (r,θ)
Trigonometry
- in both x and y dimension
- x and y coordinates change as object moves in a circle
Polar Coordinates (r,θ)
- in dimensions of radius (r) and angle (θ)
- radius stays the same while angle continuously changes
Trigonometry
- converting from polar to cartesian coordinates
- sin θ = opposite/ hypotenuse --> y = r*sinθ
- cos θ = adjacent/ hypotenuse --> x = r*cosθ
- converting from Cartesian to Polar coordinates
- r = sqrt(x^2 + y^2)
- θ = arctan(y/x)
Linear Motion vs Circular Motion
Angular Position
Angular Velocity (ω) & Tangential Velocity
As radius increases, tangential velocity will increase. Uniform Circular MotionAn object travels in a circle with radius (r) with constant speed (v)
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- Velocity is changing because direction of the object's speed is changing
- Because velocity is changing, the object is accelerating.
- Because the object is accelerating, there is a force providing acceleration, which is...
Centripetal Acceleration
Relation to Force
Without centripetal force, the object will go into tangential (linear) motion in the direction it was last at because nothing is keeping it traveling in a circle anymore. As mass increases, the centripetal force will increase. As velocity increases, the centripetal force will increase. As radius of circular motion increases, the centripetal force will decrease. As force increases, the radius of curvature will increase. |
Universal Gravitation
If two objects have mass, there exists a force of gravity between the two objects.
The force of gravity depends on two factors
The force of gravity depends on two factors
- the mass of each object -- proportional
- the distance between the center of mass of the two objects -- inversely proportional to the square of
- This distance may sometimes be the radius, but not always.
Newton's Universal Law of Gravitation
Everything with mass attracts every other thing with mass in the universe. Gravity is proportional to mass of each body and inversely proportional to the square of the distance between the center of mass of two bodies.
Universal Gravitational Constant: 6.67 * 10^-11 N*m^2/kg^2
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Gravitational Field
Mass creates a field to determine how the mass interacts with the field source
Height is very small compared to the radius of the Earth, so the gravitational field is considered to be constant
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Gravitational field is not constant and not parallel when the radius increases and the object is not on the surface of the Earth.
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Types of Masses
Inertial Mass
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Gravitational Law
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Circular Orbit
Circular orbit: an orbit with a constant circular radius traveling with a constant speed.
If moving fast enough, an object will have a force constantly pulling it toward the center while it keeps trying to travel in a tangential direction. Thus, the object is constantly changing its direction of movement, undergoing orbital motion, which is essentially circular motion. Consequently, the object is almost "constantly falling" or has a feeling of weightlessness.
This explains why people in space stations that are orbiting the Earth feel weightless, but still feel the force of gravity by the Earth on the space station.
If moving fast enough, an object will have a force constantly pulling it toward the center while it keeps trying to travel in a tangential direction. Thus, the object is constantly changing its direction of movement, undergoing orbital motion, which is essentially circular motion. Consequently, the object is almost "constantly falling" or has a feeling of weightlessness.
This explains why people in space stations that are orbiting the Earth feel weightless, but still feel the force of gravity by the Earth on the space station.