Two cars start from rest from point A on a circular track of radius r=200 m. The

Question

Two cars start from rest from point A on a circular track of radius r=200 m.  They travel in opposite directions with constant but different tangential accelerations and meet again at point B 10 seconds after they started moving.  The angle traveled by the red car is Theta = 120 degrees.  (Hint: you need to use radians in your equations)

a) Find the angular acceleration of the blue car in rad/sec^2.

b) Find the angular speed of the red car at point B.

c) Find the centripetal acceleration of the blue car at point B.

Explanation / Answer

a.

Since read car moved 120 degrees, and the total track was 360 degress, blue cart mjust have moved = 360 -120 = 240degress or 4 pi /3 radians. here, angle covered = 4pi / 3 ; initial angular speed = 0 and time = 10. Using s= ut + 0.5at^2 for angular motion, 2pi/75 rad/sec.

b. using s = (v + u)*t/ 2 for angualr motion, v = 2pi/15 rad/s.

c. centripetal acceleration = v^2 * r where v is the angualr velocity(denoted by omega usually). speed of blue car = 4pi/15 rad/s. This can be ontained by using the same method as in b. so acceleraton = 70.18 m/s^2

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