# LECTUR~6_12.9 - A radar gun at O rotates with the angular...

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A radar gun at O rotates with the angular velocity of θ = 0.1 rad/s and angular acceleration of θ = 0.025 rad/ s 2 , at the instant θ = 45°, as it follows the motion of the car traveling along the circular road having a radius of r = 200 m. Determine the magnitudes of velocity and acceleration of the car at this instant. r 200 m O u

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If a particle’s position is described by the polar coordinates r = (2 sin 2 θ ) m and θ = (4t) rad, where t is in seconds, determine the radial and transverse components of its velocity and acceleration when t = 1 s.
DR. SANISAH SAHARIN (E1-5-2.14) MEC 1392 DYNAMICS LECTURE 1: SECTION 12.9

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ABSOLUTE DEPENDENT MOTION ANALYSIS OF TWO PARTICLES Today s Objectives : Students will be able to: 1. Relate the positions, velocities, and accelerations of par ticles undergoing dependent motion. In-Class Activities : Applications Define Dependent Motion Develop Position, Velocity, and Acceleration Relationships
APPLICATIONS The cable and pulley system shown can be used to modify the speed of the mine car, A, relative to the speed of the motor, M. It is important to establish the relationships between the various motions in order to determine the power requirements for the motor and the tension in the cable.

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APPLICATIONS (continued) Rope and pulley arrangements are often used to assist in lifting heavy objects. The total lifting force required from the truck depends on both the weight and the acceleration of the cabinet.
DEPENDENT MOTION (Section 12.9) In many kinematics problems, the motion of one object will depend on the motion of another object. The motion of each block can be related mathematically by defining position coordinates , s A and s B . Each coordinate axis is defined from a fixed point or datum line , measured positive along each plane in the direction of motion of each block. The blocks in this figure are connected by an inextensible cord wrapped around a pulley. If block A moves downward along the inclined plane, block B will move up the other incline.

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DEPENDENT MOTION (continued) In this example, position coordinates s A and s B can be defined from fixed datum lines extending from the center
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• Fall '13
• Acceleration, Velocity, fixed length, SB, dependent motion

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