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California University of Pennsylvania *

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1500

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Aerospace Engineering

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Oct 30, 2023

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Chapter 2 formulas Freely Falling Bodies: In free-fall motion, an object experiences negligible air resistance and a constant acceleration due to gravity with a magnitude of approximately 9.80 m/s 2 pointing downward near Earth's surface: g = -9.8 m/s 2 Graphical Analysis of Velocity & Acceleration: The slope of a plot of position versus time for a moving object gives the object's velocity. The slope of a plot of velocity versus time gives the object's acceleration. [Instantaneous] velocity average acceleration [Instantaneous] acceleration Displacement is a vector that points from an object's initial position to its final position. The magnitude of the displacement is the shortest distance between the two positions. Initial positions and times = 0 average velocity

Chapter 3 formulas Average Velocity (Parallel to change in r) Instantaneous Velocity is Tangent to trajectory curve Average Acceleration (Parallel to change in v) Equations of Kinematics 0 v v at = + ( ) 1 2 0 x v v t = + 2 2 0 2 v v ax = + 2 1 2 0 x v t at = + 0 y y y v v a t = + 2 1 2 0 y y y v t a t = + ( ) 1 2 0 y y y v v t = + 2 2 0 2 y y y v v a y = + The above assumed initial positions of zero Chapter 3 formulas

Newton’s 1st Law : An object at a constant speed (which could be 0) remains at constant speed unless acted upon by a non-zero net force. Inertia is the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line. The mass of an object is a quantitative measure of inertia. Newton’s 2nd Law Newton’s 3rd Law: Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. Chapter 4 formulas 1 2 2 = m m F G r 11 2 2 6.673 10 N m kg − = × ⋅ G = W mg 2 = E M g G r The normal force F N is one component of the force that a surface exerts on an object with which it is in contact – namely, the component that is perpendicular to the surface. Apparent Weight equals the normal force for an object on a scale. MAX s s f f ≤ MAX s s N f F μ = Static friction Kinetic friction μ = k k N f F

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Chapter 5 Formula Sheet 2 r v T π = 2 v v t r Δ = Δ c a = 2 c c v F ma m r = = 2 tan v rg θ = 3 2 2 E r T GM π = E GM v r = Banked Curves Orbital motion Vertical Circular Motion Circular Motion