1nd Edition PHY 101 Lecture 19 Outline of Last Lecture I Elastic Collision in 1D II 6 4 Glancing Collisions III Problem Solving 2D Collisions IV Chapter 7 Rotational Motion V 7 1 Angular Speed and Angular Acceleration VI Rigid Body VII Sign of Angular Displacement Speed Acceleration Outline of Current Lecture VIII 7 2 Rotational Motion Under Constant Angular Acceleration IX 7 3 Angular Linear Quantities a Tangential Speed Acceleration X 7 4 Centripetal Acceleration a Centripetal Tangential Acceleration Current Lecture 7 2 Rotational Motion Under Constant Angular Acceleration Kinematic equations for rotational motion read similar to those of linear motion o i at o it at2 o 2 i2 2a example o a wheel rotates with a constant angular acceleration of 3 5 rad s 2 o at t 0 the wheel s angular speed is 2 0 rad s o a what is the wheel s angular speed at t 2s o through what angle does the wheel rotate from t 0 and t 2s o solution a i at 2 0 3 5 2 9 0 rad s b it at2 2 0 2 3 5 2 2 11 0 rad 7 3 Angular Linear Quantities These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Rigid body every point has the same angular displacement speed and acceleration When an object rotates o The arc length linear distance s r depends on the position r of a point I the rigid body The velocity is tangential to its trajectory Tangential speed o Vi s t r t r Tangential acceleration o r vi t r t Tangential Speed Acceleration Tangential speed v r Acceleration i r The farther away a point from the rotational axis the greater its tangential speed acceleration will be example tangential speed and acceleration o a CD rotates from rest with a constant angular acceleration to an angular speed of 31 4 rad s in 0 9 s o A what is the angular acceleration o B through what angle does the disk rotate within the 0 9 s o Solution A i at 31 4 at a 31 4 0 9 34 9 rad s2 B it at2 34 9 0 9 2 14 1 rad o C the radius of the disk is 4 45cm a tiny bug rides the rim of the disk What is the tangential acceleration of the bug at t 0 9 s V r 31 4 4 45 x 10 2 1 4 m s Tangential acceleration A r 34 9 4 45 x 10 2 1 55 m s2 o What is the distance the bug rides during the 0 9s Solution from part b we have at 0 9s 14 1 rad the distance the bug rides x r 4 45 x 10 2 14 1 0 63 m 7 4 Centripetal Acceleration An object travelling in a circle even though it moves with constant speed it will have acceleration The centripetal acceleration is due to the change in the direction of the velocity o A vf vi t Centripetal center seeking it can be shown that the direction of the velocity change points toward the center Therefore the acceleration is directed toward the center of the circular motion For a constant speed circular motion the magnitude of the centripetal acceleration is o Ac v2 r v tangential speed Do not confuse the centripetal acceleration with the tangential acceleration that we discussed earlier Tangential acceleration is due to the change in the tangential speed Centripetal acceleration is due to the change in the direction of velocity Centripetal Tangential Acceleration Tangential speed v r o Ac v2 r r 2 r r 2 If the object is doing varying speed circular motion then we have both tangential acceleration at centripetal acceleration ac The magnitude of the total acceleration satisfies the Pythagorean theorem
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