Unformatted text preview: All figures/diagrams/illustrations used in these lecture slides are copyrighted materials from the text book adopted for this module: Physics for Scientists and Engineers with Modern Physics, Serway th & Beichner (5 ed.) or Serway & Jewett th (6 ed.) These lecture slides are strictly for use related to the PC1431 Physics IE module. Any other use, including external Lecture 04 Uniform Circular Motion & Relative Motion Objectives
Understand the properties of uniform circular motion. Understand tangential and radial acceleration. Able to describe relative motion and solve related problems. Understand the concepts of inertial and non inertial frames. Uniform Circular Motion Acceleration occurs when there is a change in magnitude and/or direction of velocity. Recall: Uniform circular motion occurs when there is a change of direction of velocity only, i.e. the object moves at constant speed. Uniform Circular Motion Centripetal Acceleration In general for a particle moving along a curved Tangential & Radial Acceleration path, the velocity changes in both magnitude and direction. The total acceleration vector is a vector sum of the radial and tangential components: Tangential & Radial Acceleration The tangential acceleration causes the change in the speed of the particle, it is parallel to the instantaneous velocity, and its magnitude is The radial acceleration arises from the change in direction of the velocity vector and has an absolute magnitude given by Unit Vectors is a unit vector lying along the radius vector and directed radially outward from the center of the circle. is a unit vector tangent to the circle. Its direction is in the direction of increasing . Unit Vectors r and Relative Motion The velocity and acceleration of an object depend on the frame of reference in which it is measured. Relative Motion Frame of reference (S, S', ...) Observers in different frames of reference may describe the motion of an object differently (in terms of displacement, velocity, acceleration ...) If the physics the same in all frames of reference? Galilean Coordinate Transformation Consider two frames: S : fixed relative to earth S' : moving at velocity v0 relative to S Assume origins of S and S' coincide at t =0 The displacements of the particle P in S (r) and S'(r') are related by: Galilean Velocity Transformation Differentiating These Galilean transformation equations relate the coordinates and velocities of a particle measured in frames S and S' Inertial Frames of Reference Differentiating The physics in two different inertial frames of reference is the same Example
A boat heading due north crosses a wide river with a speed of 10.0 km/h relative to the water. The water in the river has a uniform speed of 5.00 km/ h due east relative to the Earth. Determine the velocity of the boat relative to an observer standing on either bank. Noninertial Frames of Reference An inertial system is one in which a free body experiences no acceleration The laws of mechanics must be the same in all inertial frames of reference, i.e. the results of an experiment is similar in all inertial frames A free body in a noninertial system experiences acceleration, i.e. frame is accelerating with respect to "earth" Common examples: observer in an accelerating lift, merrygoround, swing ... Relative Motion at High Speeds Galilean transformations are only valid when the particle speeds v << c (speed of light). As v c, these transformation equations are replaced by the Lorentz (relativistic) transformations (Einstein's Special Theory of Relativity) which predicts that v cannot exceed c. Relativistic transformations at v << c reduce to the Galilean transformations (Bohr's correspondence principle), not vice versa. ...
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