December 2017 - Page 3 of 8 - Shawn Zhong - 钟万祥

2.4 – Circular & Relative Motion

Radians and Degrees • In degrees, once around a circle is 360° • In radians, once around a circle is 2π • A radian measures a distance around an arc equal to the length of the arcs radius • Δs=C=2πr Linear vs. Angular Displacement • Linear position / displacement given by Δr or Δs • Angular position / displacement given by Δθ • s=rθ • Δs=rΔθ Linear vs. Angular Velocity • Linear speed / velocity given by v ⃗ • Angular speed / velocity given by ω ⃗ • v ⃗=(ds ⃗)/dt • ω ⃗=(dθ ⃗)/dt Direction of Angular Velocity Converting Linear to Angular Velocity Linear vs. Angular Acceleration • Linear acceleration is given by a ⃗ • Angular acceleration is given by α ⃗ • a ⃗=(dv ⃗)/dt • α ⃗=(dω ⃗)/dt Centripetal Acceleration Reference Frames • A reference frame describes the motion of an observer ○ Most common reference frame is Earth • Laws of physics we study in this course assume were in an inertial, non-accelerating reference frame • There is no way to distinguish between motion at rest and motion at a constant velocity in an inertial reference frame Calculating Relative Velocities • Consider two objects, A and B. • Calculating the velocity of A with respect of reference frame B (and vice versa) is straightforward • Example: ○ Speed of car with respect to the ground ○ Walking on a train, speed of a person with respect to the train • v_(A with respect to C)=v_(A with respect to B)+v_(B with respect to C) Linear vs. Angular

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3.1 – Newton’s First Law & Free Body Diagrams

Newtons First Law of Motion • An object at rest will remain at rest, and an object in motion will remain in motion, at constant velocity and in a straight line, un line acted upon by a net force • An object will continue in its current state of motion unless an unbalanced force acts upon it • An object at rest will remain at rest unless an unbalanced force acts upon them • Also known as the law of inertia Force • A force is a push or pull on an object • Unites of force are newtons (N) • 1N=1 (km×m)/s^2 Contact Force Field Force Tension Applied Force Friction Gravity Electrical Force Magnetic Force Net Force • A net force is the vector sum of all the forces acting on an object • If all forces are balanced, there is no net force. This situation is known as translational equilibrium • An unbalanced force is a net force Equilibrium • Static Equilibrium ○ Net force on an object is 0 ○ Net torque on an object is 0 ○ Object is at rest • Mechanical Equilibrium ○ Net force on an object is 0 ○ Net torque on an object is 0 • Translational Equilibrium ○ Net force on an object is 0 Inertia • Inertia is the tendency of an object to resist a change in velocity • Mass actually has two aspects ○ Inertial mass is how hard it is to change an objects velocity ○ Gravitational mass is how strongly a gravitational field affects a mass • For the purposes of basic introductory physics, mass and inertia are synonymous Free Body Diagrams • Tools used to analyze physical situations • Show all the force acting on a single object • Object itself drawn as a dot or rectangle

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3.2 – Newton’s Second & Third Laws of Motion

Newtons Second Law of Motion • The acceleration of an object is in the direction of and directly proportional to the net force applied, and inversely proportional to the objects mass • Valid only in inertial reference frames. • F ⃗_net=∑▒F ⃗ =ma ⃗ Mass vs. Weight • Mass is the amount of

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3.3 – Friction

Coefficient of Friction • Ratio of the frictional force and the normal force provides the coefficient of friction • μ=F_f/F_N Kinetic or Static Calculating the Force of Friction • The force of friction depends only upon the nature of the surface in contact (μ) and magnitude of the normal force FN • Combine with Newtons Second Las and FBDs to solve more involved problems 2007 Free Response Question 1

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3.4 – Retarding & Drag Forces

Retarding Forces • Sometimes the frictional force is a function of an objects velocity (such as air resistance) • These forces are called drag, or retarding, forces. The Skydiver • Assume we drop Alex from an airplane • Typically the drag forces on a free-falling object take the form F_drag=bv or F_drag=cv^2, where b and c are constants • For this problem, lets assume F_drag=bv Velocity as a Function of Time Acceleration as a Function of Time Graph of Acceleration, Velocity, and Displacement 2005 Free Response Question 1 2013 Free Response Question 2

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