Engineering Mechanics: Dynamics Part 1

Learn the basics of dynamics by contrasting kinematics and kinetics, and define mass, weight, force, particle, rigid body, scalars, vectors, as well as dot and cross products.

Newton's laws describe motion: net zero force yields constant velocity. Sum of forces equals mass times acceleration, and action–reaction forces are equal and opposite; weight equals mass times gravity.

This lecture defines planar versus rectilinear motion, introduces displacement s(t) in one plane, and derives velocity v = ds/dt and acceleration a = dv/dt = d^2s/dt^2, with sign interpretation.

Learn constant acceleration kinematics by deriving equations relating velocity, displacement, and time, including v = v0 + a t and s = s0 + v0 t + 1/2 a t^2.

Analyze a vertically fired projectile with an initial velocity of 200 m/s to determine the maximum altitude H and the time T to return to the ground, neglecting drag.

Compute the cop's pursuit: from rest to 150 km/h at 6 m/s², convert speeds, and use kinematics to find when and where he overtakes a 120 km/h speeder.

The lecture analyzes a train from station A to B, breaking motion into phases: acceleration 0.5 m/s^2 for 60 s, then 900 s at constant velocity, then deceleration to rest.

Explore nonconstant acceleration as a function of time and derive velocity from v = v0 + ∫_0^t f(t) dt, then find displacement via s = s0 + ∫_0^t v dt.

Compute acceleration from a velocity function in a straight-line dynamics problem, using ds/dt = v, integrate to find displacement, then differentiate to evaluate a at t=3 s.

Explore acceleration as a function of velocity and derive time and displacement from integrals: time equals ∫ dv / a(v); s equals s0 + ∫ v dv / a(v).

Analyze a velocity-dependent deceleration of a landing airplane using a = -k v^2, converting mph to ft/s, solving for k and stopping time over 1500 ft.

Explore non-constant acceleration as a function of displacement, derive v^2 = u^2 + 2 ∫ a ds, and relate time using ds/dt = v with integration techniques.

An example demonstrates nonconstant acceleration expressed as a function of displacement, and shows how to integrate a ds to find velocity from displacement with given initial conditions.

Explore 2D curvilinear motion in rectangular coordinates by decomposing velocity and acceleration into x and y components. Apply kinematic equations to projectile motion under constant gravity with no drag.

Explore a horizontally thrusting rocket at 800 m altitude to compute the line-of-sight angle theta to a target using two-dimensional projectile motion, time, and a horizontal acceleration of 0.5 g.

Determine the horizontal velocity vA for a tennis ball to just clear the net using y and x motion under gravity.

Analyzes two 30-degree projectile throws to hit pool edges B and C at the same instant, giving speeds 4.32 m/s and 5.85 m/s with a 0.122 s interval.

Apply normal and tangential coordinates to curvilinear motion along a path, with velocity along the tangent and acceleration split into tangential and normal components relative to the center of curvature.

analyzes a car accelerating from 50 to 100 km/h in 10 s to determine radius of curvature at point b using tangential and normal acceleration, giving r_b ≈ 163.4 m.

Analyze a car on a curved road to compute tangential and normal acceleration from a given tangential acceleration function, determine velocity, and evaluate curvature effects on overall acceleration.

Explore a baseball launched at 100 ft/s at 30 degrees, using tangential and normal components, apex timing, and radius of curvature in the projectile trajectory.

Explore polar coordinates for dynamic analysis, defining r and theta axes, deriving velocity and acceleration in polar form, including radial and theta components for curvilinear motion.

Analyze plane motion in polar coordinates by decomposing velocity and acceleration into radial and theta components, using r, r dot, and theta dot; note constant speed implies zero acceleration.

Apply polar coordinates to the moving train, and use velocity and acceleration to determine radial and theta components, i.e., r dot, r double dot, theta dot, and theta double dot.

Analyzes a slider on a rotating arm using polar coordinates, and computes velocity, acceleration, and the direction angle at t = 4 s from r(t) and theta(t).

Explore relative motion by describing a moving reference frame within an inertial coordinate system, using vectors to relate position, velocity, and acceleration.

Compute the velocity and acceleration of the train relative to the car. Convert speeds, decompose into components at 15 and 60 degrees, and apply the relative motion equations.

Analyzes a plane towing a 16 m cable at 200 km/h, using relative motion and polar coordinates to determine velocity and acceleration of the towed object at theta 15 degrees.

Compute the velocity and acceleration of car b relative to car a on a curve with radius of curvature, using tangential and normal components.