Suppose you are driving a car in a counterclockwise direction on a circular road

Question

Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is410 m (see the figure). You look at the speedometer and it reads a steady 30.5 m/s. (a) What is the angular speed of the b)Dermine the acceleration magnitude and direction of the car. c) To avoid rear end collision with the vehicle ahead you apply the brakes and reduce your angular speed to 4.8 10 2 rad/s in a t me of 3.94 s what is the tangential acceleration magnitude and d ection of the car? (a) Constant angular speed b) Decreasing angular speed 0.0743 rad/s toward the center of rotation m/s 2 opposite to the car's velocity 0.0499

Explanation / Answer

c) You need to first find the angular acceleration, alpha. If this was a linear situation, you would find the linear acceleration using the kinematic formula

Vf = Vi + a*t

The kinematic formula that works in the equivalent angular situation is

Wf = Wi + alpha*t

where Wf = 0.048 rad/s, Wi is your answer for part a(0.0743), and t is 3.94 s. Solve for alpha.

alpha = -6.675 x 10-3 rad/s2

Then, the relation between linear acceleration, a, and angular acceleration, alpha, is

alpha = a/r

So:

a = r*alpha = 410 * (6.675 x 10-3)

= 2.74 m/s2

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