Chapter 4 Kinematics in 2 Dimensions

Separate Components of Velocity

Constant Acceleration

Practice Problems Conceptual Questions –1,2,5 Problems –8,12,

Circular Motion An object moving in a circular path at a constant speed around a circle of radius, or partial circle. Velocity tangential is along the edge of circle. T is period, r – radius, and a c – centripetal acceleration

Examples Problems #26

Circular Motion in terms of angular postion, velocity, and acceleration A particle that moves at a constant speed around a circle of constant radius. Terms –Period – time per 1 revolution –Angular position (  )– position measured counterclockwise around circle –Angular displacement (  )-change of angular position. –Angular velocity (  ) – rate of change of angular displacement

Centripetal Acceleration Center seeking acceleration. An object moving at a constant speed, but moving in a circular path experiences acceleration. –A body moving within this accelerating system experiences a fictitious force called ‘centrifugal force’. –Example: As a person makes a hard turn in their car their body tends to move away from the turning direction.

Connection between angular motion and linear motion Which has a greater perimeter a circle radius of 1 m, or 2 m? 2 m When riding a carousal, who travels a greater distance the inside horses or the outside horses? Outside When playing ‘crack the whip’ on ice skates, who travels faster the person within the line of skaters or the one at the end? One at the end

Nonuniform Circular Motion Circular motion with a changing speed Positive angular displacement is considered counterclockwise displacement in a circular path. Positive angular velocity is counterclockwise motion in a circular path. Positive angular acceleration is counterclockwise acceleration as an object moves in a circular path. --  -- ++

Angular Motion vs time graphs Angular motion graphs can be treated very similarly to linear motion graphs. For Example –Slope of angular position vs time is equal to the angular velocity –Area below angular velocity vs time graph is equal to the angular displacement  t Create the angular velocity vs time graph from this graph.  t

Examples Conceptual #14 Problem #22,#33,#36

Relative Velocity Explanation Objects have velocity based on their coordinate system. Sitting here we are stationary relative to earth, but moving fast relative to moon, and faster relative to sun. V ab velocity of a with respect to b V bc velocity of b with respect to c Equation 1 to right Inverse situations below

Relative Motion Situations You are moving at 80 km/h north and a car passes you going 90 km/h. Draw the relative motion velocity vectors, and determine how the faster car appears to you. A boat heading north crosses a wide river with a velocity of 10 km/h relative to the water. The river has a uniform velocity of 5 km/h due east. Determine the boat’s velocity with respect to an observer on shore. Two planes are headed from the same airport in different directions. Airplane A is headed at 200 m/s at a direction of 30* S of W, while Airplane B is headed at 250 m/s at a direction of 60 N of E. What is the relative velocity and direction of B in relation to A? Practice Problem - 58