MCE222_LN_Sec_13-5 - EQUATIONS OF MOTION: NORMAL AND...

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EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5) Today’s Objectives : Students will be able to apply the equation of motion using normal and tangential coordinates. In-Class Activities : Hmework #3 Due March 25
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F = m a or F x i + F y j + F z k = m(a x i + a y j + a z k ) F x = ma x , F y = ma y , and F z = ma z . Newton’s second law of motion F =m a F = G(m 1 m 2 /r 2 ).
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APPLICATIONS Race tracks are often banked in the turns to reduce the frictional forces required to keep the cars from sliding at high speeds. If the car’s maximum velocity and a minimum coefficient of friction between the tires and track are specified, how can we determine the minimum banking angle ( θ ) required to prevent the car from sliding?
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APPLICATIONS (continued) Satellites are held in orbit around the earth by using the earth’s gravitational pull as the centripetal force – the force acting to change the direction of the satellite’s velocity. Knowing the radius of orbit of the satellite, how can we determine the required speed of the satellite to maintain this orbit?
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NORMAL & TANGENTIAL COORDINATES When a particle moves along a curved path , it may be more convenient to write the equation of motion in terms of normal and tangential coordinates . The normal direction (n) always points toward the path’s center of curvature . In a circle, the center of curvature is the center of the circle. The tangential direction (t) is tangent to the path, usually set as positive in the direction of motion of the particle.
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EQUATIONS OF MOTION This vector equation will be satisfied provided the individual components on each side of the equation are equal, resulting in the two scalar equations: F t = ma t and F n = ma n .
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MCE222_LN_Sec_13-5 - EQUATIONS OF MOTION: NORMAL AND...

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