Question

1.) Calculate the angular acceleration during 0-4 seconds given the following graph. 5 w (rad/s) 4 Time (sec) 2.) There are 3 cars with the same mass and same angular velocity (Srad/s) take a turn but take it in different lanes. Which statement is correct? ABC A) Car A, B, C all have the same linear velocity. B) Car A has a faster linear velocity. C) Car C has a faster linear velocity. D) Cannot determine from information 3.) Describe using impulse and momentum why air bags makes good sense in designing safe cars.

Answer 1

o Part 1: 5 4 Time 15) The angular acceleration tradest of an object is defined as rate of change of its angular velocity (w). aa do at from the graph, 5 radis at and o rad's at let Coding W, = 5 radis tis W2= o radis tz. = لا time Os. time 45. Os 45. > for time to period 0-4 seconds, angular acceleration is given by the slope of graph aso Aw At Awa دم) wi ot tz a = o-5 u- ti 5 4 rad 132. 0

or a= - 1.25 radls2. Part 2: Givena Three lanes as follows: VA Let NA, ro and ro be the radius of turns of three lanes shown. TBC وه с. clearly, raz ro7rc. and of all 3 are The angular velocities of masses cars Same a let w= angular velocity of cars. and of och each ear. mass we know, the relation between linear and angular velocities Object is z OR wxr an V= r is radius of turn (or motion of object) cars A B and Care linear velocities of respectively given by a VA = co is same w XRA w x 8B w X Xc . UB= Vc = car for each since, 8A>&B> rc VA > VB > Vc. Thus, option (B) is correcta Car A has faster linear velocity

Part 3) an push forward towards During accident the momentum of the person inside the car. Bevrácomo elppoongoden makes him [her to the stearing wheel But airbag increases the time period for which the berson pushed forward According to the definition of impulse, J = Force . X time. of time period increases force decreases The change in momentum or impulse is also large if period is force exerted on the person inside car is lesst small). ie, change longer period contributes to im in pulse. en time large and more than force