Summary of critical formulas and important facts
Summary of critical formulas and important factsPhysics 298 – Test 1Velocity and AccelerationAverage velocityv=ΔrΔt=rf- riΔtAverage accelerationa= ΔvΔt= vf- viΔtIn one dimension, instantaneous velocity (v) and acceleration (a) are the slopes (at a particular point) of the x and v versus t curves, respectively.For constant acceleration (velocity) motion, average and instantaneous accelerations (velocities) are equal.One dimensional motion under constant accelerationvf= vi+atx= vit+ 12at2x= 12vi+ vftvf2= vi2+2axFor constant velocity motion x = vtFree fall under the influence of (constant) gravitational acceleration is described by the above equations with a = -gVectorsAddition and subtraction by resolution into componentsUnit vector notation – i, j, kDot (scalar) product:a?b= abcosθabVector (cross) product:a∧b= uabsinθab where the unit vector u is at right angles to a and b whose sense is given by the right-hand rule.Projectile MotionIndependent x and y motion.Kinematic equations above represent y motion.x motion is constant velocity motion, x= vixtIf projected initial velocity (v0) is at an angle θ to horizontal then, vix = v0 cos θ and viy = v0sin θUniform Circular MotionCentripetal acceleration is given by, a = v2/R, directed towards the centre of the circleRelative VelocityV'=V+ VRNewton’s Laws of motion2nd Law:Fnet = ma( Fx = max , Fy = may , Fz = maz )1st Law: Special case of the second law when acceleration is zero. For objects at rest or in constant velocity motion there is no net force.3rd Law: For every “action” force there is an equal but opposite “reaction” force. Note that the action/reaction force pairs act on different objects.Force LawsWeight:w=mgThe weight of an object is equal to the gravitational force acting on the object. Its direction is always towards the centre of the earth.Friction:Static frictionFfs ≤ μsNKinetic frictionFfk= μkNForce of friction opposes attempted or actual relative motion of two objectsApplication of Newton’s laws via free-body diagrams.Centripetal ForceFc= mv2RDirection is always towards the centre of the circle ................
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