Dynamics Crib Sheet3

# Dynamics Crib Sheet3 - RECTILINEAR KINEMATICS(straight line...

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RECTILINEAR KINEMATICS (straight line motion of particles) RECTILINEAR KINEMATICS (constant acceleration) PROJECTILE MOTION (same as Rectilinear Kinematics above, but ) Curvilinear Motion ( (Two forms of problems) Path Given (in x-y plane) y=f(x), use chain rule to find vx, ax, vy, ay (2 of these must be known in order to solve) CHAIN RULE EXAMPLE: is given as a path equation. Find the 1st and 2nd time derivatives of this equation. Parametric Equations Given: can be R (t), v (t), or a (t) n-t acceleration or and Instantaneous Center (IC) Method : v B = v B/IC v B/IC = ϖ x r B/IC RIGID BODY MOTION and FIXED AXIS ROTATION Angular motion Constant α Fixed Axis Rotation – motion of a POINT r v ϖ = MESHED GEARS ω=dθ/dt α=dω/dt Arc Lengths Velocities Tangential accelerations WORK ENERGY = + - 2 2 1 1 T U T U Force = Fcosθ * distance U Force = ds F S S 2 1 cos θ U weight = +/-mg(h 2 -h 1 ) U spring = -(1/2)k ) ( 2 1 2 2 s s - U constant couple = m (Δθ If m is not constant, U couple = θ θ θ d m 2 1 T = 2 2 2 1 2 1 ϖ G G I mv + POWER

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• Spring '06
• GRANTHAM
• DT DT DT

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