Physics and Math 1 Kinematics and Dynamics

Physics and Math 1: Kinematics and Dynamics Vectors and Scalars Forces and Acceleration Vectors: Physical quantities that have both magnitude and direction. Examples: displacement, velocity, acceleration, and force Scalars Quantities without direction. Scalar quantities may be the magnitude of vectors, like speed, or may be dimensionless, like coefficients of friction Vector Addition: Tip-to-tail method, or you can break the vector into its component parts and use Pythagorean theorem Vector Change the direction of the subtracted vector and then Subtraction: do a tip-to-tail addition Vector By scalar: Changes the magnitude and may reverse the Multiplication: direction. Dot Product: 𝐴"• "𝐵= |𝐴|| 𝐵| "cos"(q) , results in a scalar quantity Cross Product: 𝐴"×"𝐵 = | 𝐴|| 𝐵| "sin"(q) , results in a new vector. Direction of the new vector can be found using the right-hand rule Force: Any push or pull that has the potential to result in an acceleration Gravity: The attractive force between two objects as a result of their masses Friction: A force that opposes motion as a function of electrostatic interactions at the surfaces between two objects Static Friction: Stationary object Kinetic Friction: Sliding object 𝑓 =𝑢"𝑁 Mass: A measure of the inertia of an object – its amount of material Weight: The force experienced by a given mass due to the gravitational attraction to the Earth Acceleration: The vector representation of the change in velocity over time. Torque: A twisting force that causes rotation t = 𝑟"𝐹sin ( q) POS"=counterclockwise NEG"=clockwise Newton’s Laws Mechanical Equilibrium Free Body Representations of the forces acting on an object. Diagrams: Translational Occurs in the absence of any net forces acting on an object Equilibrium: Rotational Occurs in the absence of any net torques acting on an Equilibrium: object. The center of mass is the most commonly used pivot point. Displacement and Velocity Displacement: The vector representation of a change in position. Path independent Distance: A scalar quantity that reflects the path traveled Velocity: The vector representation of the change in DISPLACEMENT with respect to time ./012"3456217898:0 Avg Velocity = Avg Speed = ./012"0498 ./012"34501:78"0;1<8283 ./012"0498 Instantaneous Velocity: The change in displacement over time as the time approaches 0 Instantaneous Speed: The magnitude of the instantaneous velocity vector First Law: An object will remain at rest or move with a constant velocity if there is no net force on the object Fnet = m a = 0 if at rest or constant velocity Second Law: Any acceleration is the result a net force > 0 Fnet = m a Third Law: Any two objects interacting with one another experience equal and opposite forces as a result of their interaction FAB = -FBA Motion with Constant Acceleration Linear Motion: Includes free fall and motion in which the velocity and acceleration vectors are parallel or antiparallel Kinematics Equations for Linear Motion 𝑣P =𝑣Q +𝑎"∆𝑡 ∆𝑥=𝑣Q "∆𝑡+" X 𝑣P ∆𝑥 ="𝑣Z"∆𝑡 =𝑣QX +2"𝑎"∆𝑥 W X "𝑎"(∆𝑡)X (if a = 0) Projectile Contains both an x- and y-component. Assuming Motion: negligible air resistance, the only force acting on the object is gravity. X velocity is constant throughout. Inclined Planes: Force components: Parallel to the ramp use sinq. “Sin is sliding ¯ the slide”. Perpendicular to the ramp use cosq. Circular Best thought of as having radial and tangential Motion: dimensions. Centripetal force vector points radially inward, the instantaneous velocity vector points tangentially. Centripetal force: 𝐹7 =" 9"<[ ;