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Reviewing Terms & Formulas 1. Velocity – is always in the direction of the movement Velocity v = d/ t + direction 2. Acceleration – is change in velocity - over time. Any change – speeding up ( positive accel.) - slowing down ( neg. accel. ) - changing directions is a change in velocity too! Accel a = Δv / t + direction Δv = ( Vf – Vi ) DID YOU KNOW: There is a scientific term for acceleration in a circular path? Centripetal acceleration! Centripetal acceleration – acceleration of an object in circular motion. It is directed toward the center of the circular path. Oh yeah & it has a formula ! Cool : ) 2 v ac = r ac = centripetal acceleration, m/s2 v = tangential speed, m/s r = radius, m Before you can complete the Centripetal Acceleration Formula ……. You must solve for v. v= tangential speed ( m/s) Solving for v is done a special way for circular motion. Let’s break down the term “tangential speed” Root word “Tangent” a straight line (LINEAR) or plane that touches a curve or curved surface at a point but does not intersect it at that point 2nd word “Speed” d / t For a constant tangential speed: v = tangential speed, m/s d 2πr v= = t T d = distance, m t = time, s r = radius, m T = period, s, Time passing for one revolution is called period Now we have to put all the formula components together on a diagram for it to make sense. 1st - Let’s review RADIUS…. What is it and how do you measure it? Radius = r r 2nd – we have to add the velocity component Remember • velocity follows the path! Path - Straight line off a circle • AND velocity is called: tangential speed VELOCITY = v ( tangential speed) r v Oh yeah – lets go over T. T = time it takes for the obj. to complete 1 revolution ( see diagram below ) Start Stop Now, if you cannot time 1 revolution, you can time 3 - 5 revolutions. Then, divide the total time by the # of revolutions to get the T of 1 revolution. Example of solving for T You Hula Hoop for 4 seconds and the hoop makes 5 revolutions. 4 secs / 5 revolutions = 1 revolution = .8 sec 3rd –We can now solve for centripetal acceleration Remember Acceleration is primarily toward the center of the circle. Centripetal Acceleration = ac Remember to check the units to determine if you need to solve for V using the formula in the Yellow Box before you can complete the formula for centripetal acceleration!! 2 v ac = r 2πr v= T Problem 1: If tangential velocity is 10 m/s and the radius is 2m, find ac. Problem 1 – Solution V = 10 m/s r =2m ac = ? m/s2 Formula 2 v ac = r ac = (10 m/s )2 =100 m2 / s2 = 50 2m 2m m/s2 Problem 2: ( Please read carefully!! ) A 400 kg car takes 8 seconds to travel a circle of radius 60m. Find ac . Did you read carefully…. m not necessary to solve 8s = T r = 60 m ac = ? m/s2 Problem 2 Solution 2 v ac = r 2πr v= T v = 2(3.14) 60 m = 377 m = 47.12 m/s 8s 8s ac = (47.12 m/s)2 = 2222.3 m2 /s2 60m =37 m/s2 60 m Now lets move on to ….. Centripetal Force!!! May the Force B W/ U! Centripetal Force – the net inward force that maintains the circular motion of an object. There are 2 formulas to solve for Fc . Choose 1. Fc = m a c Fc = centripetal force, N m = mass, kg ac = centripetal acceleration, mv Fc = r 2 m/s2 v = tangential speed, m/s r = radius, m r Fc = m a c m v2 Fc = r v FYI: Centripetal Force is a NET FORCE. There are different types of NET FORCES involved with Centripetal Force. A car going around a curve on a flat road: Fc = Ff (friction force) Orbital motion, such as a satellite: Fc = Fg (weight or force of gravity) • A person going around in a spinning circular room( Barrel of Fun ): Fc = FN (normal force) A mass on a string (horizontal circle, i.e.. parallel to the ground): Fc = F (tension force in the string) T FYI: Centrifugal Force an APPARENT FORCE that SEEMS to pull a rotating or spinning object AWAY from a CENTER. Often referred to as the “ Fictional Force” because it is NOT REAL!! Torque – a quantity ( Force ) that causes rotational accel. of an object. Formula: τ = Fr r = radius Units: Nm or Fd or d = dist. Nm Which has more tangential speed? Object 1 Object 2