Question

Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r 28 m/s (about 63 mi/h) 385 m (see the figure). You look at the speedometer and it reads a steady T(decreasing) (a) Constant angular speed (b) Decreasing angular speed Concepts (i) Does an object traveling at a constant tangential speed (for example, vT= 28 m/s) along a circular path have an acceleration? Yes No (ii) Is there a tangential acceleration aT when the angular speed of an object changes (e.g, when the car's angular speed decreases to 5.5 x 10 rad/s)? Yes No Calculations (a) What is the angular speed of the car? (Enter the angular speed when traveling at constant angular speed. Enter your answer to at least 4 significant figures.) rad/s (b) Determine the acceleration (magnitude and direction) of the car. (Enter the acceleration when traveling at constant angular speed.) m/s2 magnitude | ---Select- direction (c) To avoid a rear-end collision with the vehicle ahead, you apply the brakes and reduce your angular speed to 5.5 x 10 rad/s in a time of 4.0 s. What is the tangential acceleration (magnitude and direction) of the car? (Enter the tangential acceleration over the full 4.0 s.) m/s2 magnitude Select direction

Answer 1

Here we apply concept of circular motion and equation of motion for constant angular acceleration as well as relation between linear velocity and tangential velocity.

= 385 m = 28 m/s q - At Akta Along a circular path wit tangential speed as cone fant but direction of velocity is alwaxe changing to move in circle so we can eay speed de constant but velocity to changing acceleration I = SE so ãto Yee so obiect will have acceleration but it will be radial acceleration It tangential speed is also change or angular speed is changing then there will be acceleration along the direction of velocity either atory on opposite to velocity Yes there will be tangential acceleration a We know, w=wr - w = angular speed w = u 28 m/s) - a or Tren - 10 = 0.07273 radleec. 1 At contant angular speed; no tangential acceleration. a = 6 t

au = 28 ms) = 2.0364 miz 385m ! As radial acceleration will always be towards center of circle no firection de perpendicular to tangent cial speed: (aj Initial cingulax_speed, we =0:07273 radale I final angular speed, we=5.5X202 sadfree time, t= 4.0 sec angular acceleration = d. -> W = We tot → 5:5x16? =0.07273 + (4) => x=-0.004433 rad seel Hangential acceleration, Let=lar. =(0.004433) (385. = po 706 M/S2 - Direction will be opposite to tangential speed se. 180° to tangential speed as tangential accelercetion is negative