Question

In: Physics

Two people start at rest from the same point on a circular track of radius R...

Two people start at rest from the same point on a circular track of radius R = 20 m. Person #1 runs counterclockwise around the track with a con- stant angular acceleration of α1 = 0.0010 rad/s2. At the same time, Person #2 runs clockwise around the track with a constant angular acceleration of α2 = 0.0025 rad/s2. Determine the speed of each person when they meet for the first time after they start running.

I know from the class to start by finding time when they meet using |θ1| + |θ2| = 2π yielding 1/2 α1(T)^2= 1/2 α2 (T)^2

can you please solve this problem

Also explain why |θ1| + |θ2| = 2π and

Where this equation come from 1α1T2 + 1α2T2 = 2π

Solutions

Expert Solution

Total angle in a circle is

Person 1 and Person 2 start from rest at same point, move in a circle . When the two meet , magnitude of angular displacement of person 1 is and magnitude of angular displacement of person 2 is , then

The two persons meet after time

Equations for angular displacement are ----(1) and ---(2)

Initial angular speed of two persons is zero. --(3)

( the two persons start from rest)-

----(4)

Using equations (1) , (2) (3) and (4)

Angular speed of person 1 after time T is

Angular speed of person 2 after time T is

Linear speed of person 1 after time T is

Linear speed of person 2 after time T is

genius_generous answered 1 year ago

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