Tiêu đề Material - Engineering Mechanics (Dynamics).docx ✅

SPECIAL TOPICS III DYNAMICS Dynamics is the branch of mechanics that deals with bodies in motion. Motion is a progressive change of position of the body. Kinematics is the branch of dynamics which describes the motion of bodies without reference to the forces that either cause the motion or are generated as a result of motion. Kinematics is often referred as geometry of motion. Rectilinear motion a type of motion in which the body moves in a straight line or is moving in the direction parallel to its displacement. RECTILINEAR MOTION (Kinematics in one-dimension) Uniform Motion – A motion with constant speed and motion. Uniformly accelerated motion – A motion with constant change in velocity or of uniform acceleration Note: a is positive when accelerating, and negative when decelerating. Free Falling Body – A motion whose constant change in velocity is with respect to gravity. It does not account air resistance. PROJECTILE (Kinematics in Two-Dimensions) Projectile – A body which after being given an initial velocity (with an initial angle of release), is allowed to travel under the action of gravity alone. Components: Horizontal Components: Vertical Components: Multiple components: CURVILINEAR MOTION Angular Displacement () is the angle through which a rigid object rotates about a fixed axis. SI Unit: radian (rad) Radian is the Si unit of displacement defined as the circular arc length (S) traveled by point of a rotating body divided by the distance (r) of the point from the axis. 2. 2π rad = 360 degrees 1 revolution
Average angular velocity () is the angular displacement of an object divided by the time elapse. SI Unit: rad/s Instantaneous angular velocity is the angular velocity that exists at a given instant. SI Unit: rad/s Angular acceleration () is the change in angular velocity divided by the time elapsed. SI Unit: rad/s² Tangential velocity (V i ) is the linear velocity of a tangent point on a rotating body. It represents how fast the point is moving along the arc of the circle. SI Unit: m/s Tangential acceleration (a t ) the linear acceleration of a tangent point on a rotating body. SI Unit: m/s² Uniform circular motion is the movement of a point particle at constant tangential speed in circular path CURVILINEAR TRANSLATION Normal Tangential Conical Swing Banking (Ideal angle w/ no friction) Banking (at greatest speed) Impulse and Momentum Impulse (I) is the product of the average force and the time interval during which the force acts. Momentum (P) is the product of the mass and velocity. Collision refers to the mutual action of the molecules, atoms, and etc., when they encounter one another. Momentum is conserved in all collisions or explosions. In the conservation of momentum; the final total momentum is equal to the initial total momentum. The essential effect of collision is to redistribute the total momentum of the colliding objects. All collisions-conserve momentum, but not all of them conserve kinetic energy as well. Law of Conservation of Momentum The momentum of the body before the impact is equal to the momentum of the body after the impact Collision falls into three categories: A. Elastic (e = 1) B. Inelastic (0 < e < 1)