CE 002Friday, November 21, 2014 8:01 AM Projectile: 1. Horizontal Velocity with no angle: Voy = 0 2. Alpha: 3. 4. 5. 6. -Vosin When it reaches the ground, Y = 0 When it reaches the highest height, Vy = 0. Air resistance is negligible. *Always negative ang g on all projectile. *Always check the units. If it is in feet, g then is equal to 32.2 ft / s2 *Convert all units to meters or feet and then seconds. *If there are a lot of things to "pass" first before reaching destination, choose the bigger Velocity. A projectile is fired from the edge of a 150-m cliff with an initial velocity of 180 m/s at an angle of 30° with the horizontal. Neglecting air resistance, find (a) the horizontal distance from the gun to the point where the projectile strikes the ground, (b) the greatest elevation above the ground reached by the projectile. Answers: a) x = 3100 m, b) 513 m CE 002 Page 1 Chapter 15 Types of Rigid Body Motions 1. Translation: if any straight line inside the body keeps the same direction during the motion and along parallel paths a. Rectilinear Translation: moved on straight line paths. b. Curvilinear Translation: moved on curved line paths. *Thus, when a rigid body is in translation, all the points of the body have the same velocity and the same acceleration at any given instant. *Curvilinear Translation: the velocity and acceleration change in direction as well as in magnitude at every instant *Rectilinear Translation: the velocity and acceleration is the same. 2. Rotation about a Fixed axis: particles forming the rigid body move in parallel planes along circles centered on the same fixed axis called axis of rotation. *If the axis of rotation intersects the rigid body, the particles located on the axis have zero velocity and zero acceleration. On (A), all particles are moving along parallel circles. Any given straight line drawn on the plate will maintain the same direction. CE 002 Page 2 plate will maintain the same direction. On (B), all particles are moving along concentric circles. Point 0 remains fixed. θ is positive when counter clockwise. *Divide velocity / acceleration by radius to get the rad unit. *Divide the distance by 2pi to get the number of revolutions. Problem Solving: 1. Uniform Rotation: Acceleration is zero. 2. Uniformly Accelerated Rotation: Acceleration is constant *Kapag inextensible, the velocity and acceleration of point A and point B is the same. 3. General Plane Motion: Any motion that is neither a rotation nor a translation. (e.g. Rolling wheel and sliding rod.) *sum of a translation and a rotation CE 002 Page 3 4. Motion About a Fixed Point: The three-dimensional motion of a rigid body attached at a fixed point 0, e.g, the motion of a top on a rough floor. 5. General Motion: Any motion of a rigid body that does not fall in any of the categories above. CE 002 Page 4 Reviewer: CE 002 Page 5 F - Impulse and Momentum (Chapter 15) CE 002 Page 6 Reviewer: CE 002 Page 7
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