EMA 202 – Exam 1 Review 11 October 2010 Page 1 KINEMATICS Use when you want to relate changes in acceleration, velocity and distance. **Remember that the dot indicates TIME derivative Chain Rule Use you have an expression for acceleration in terms of position and you want an expression for velocity in terms of position. Usually you will plug in an expression for acceleration and then integrate. Make sure the limits on your integration match; the top values of your limits must correspond to the same point in. In addition, be sure your limits correspond to the variable behind the d. Constant Acceleration Equations Acceleration MUST be constant for these equations to apply. Projectile Motion Look at the x and y directions separately, time connects the two. Find time in one direction and use that time in the other direction. Use the constant acceleration equations. For the x direction a = 0. For the y direction a = -g. Circular Motion All the above methods may also be used for circular motion Make the following substitutions Another useful relationship for circular motion: , where s is the arc length and r is the radius.EMA 202 – Exam 1 Review 11 October 2010 Page 2 Differential of Geometric Constraints 1) Write an expression about the geometry of the situation that is always true. 2) Take the time derivative of the expression, once or twice depending on what you are looking for. **Pulley problems: Write an expression for the length of the cable. Define a datum. Relative Motion Use when you want to relate the motion of two objects moving with respect to each other. B/A means B with respect to A or the vector from A to B. Coordinate Systems Choose a coordinate system other than Cartesian in order to simplify calculations. Normal-Tangential Tangent unit vector is parallel to the velocity vector. Normal unit vector is perpendicular to the tangent unit vector and points towards the concave side of the curve. (FYI: for 3D motion ) Polar Must pick an origin when using polar coordinates. The radial unit vector points from the origin to the point. The theta unit vector is perpendicular to the radial unit vector and points in the direction of increasing theta.EMA 202 – Exam 1 Review 11 October 2010 Page 3 NEWTON’S SECOND LAW Use when you want to relate forces to accelerations. Sum the forces in the directions of the coordinate system you are using. Plug the acceleration expressions for the specific coordinate system you are using into Newton’s second law equation. Force Laws Linear Springs Where k is the spring constant, L is the current length and L0 is the unstretched length. Friction Sliding No Slip Impending SlipEMA 202 – Exam 1 Review 11 October 2010 Page 4 ENERGY METHODS Use when you want to relate changes in position to changes in velocity. Must be looking at two different points in time. Scalar equations. If you are looking at the energy of a system of bodies, you must look at the kinetic and potential energy of each body. Kinetic Energy Work Potential Energy/Work done by Conservative Forces Non-path dependent forces. The work term can be simplified for these types of forces, by looking at the potential energies at each state. Linear Spring Terrestrial Gravity Problem Solving Strategy 1) Draw a picture of each state or label each state 2) Define a datum for gravitational potential energy 3) Write out full work energy equation 4) Indentify all forces (conservative, non-conservative or