Two bodies, c1 and c2, begin to move from the same point at constant angular velocity, but in opposite directions, along a 30 m radius circumference. If the first one takes 20 seconds to complete a rotation and the second takes 60 seconds, calculate:
a) The time that they take to meet.
b) The angle and distance traveled by each one.
R = 30 m
T1 = 20 s
T2 = 60 s
Since their trajectory is a circumference and their angular velocities are constant we face a problem of uniform circular motion or u.c.m.
Since we know the period of each one, we can calculate the angular velocities by means of the following equation:
Both bodies will meet each other before completing a rotation. In particular, when they meet the sum of their angular positions will be exactly 2π radians.
If we use the equation of position of , and substitute, we get:
Knowing that similarly , then:
If we replace the time at which they meet (t = 15 s) and the angular velocity in the equation of position of , we get that the angle traveled by c1, which is:
And that the angle traveled by c2 is:
To calculate now distance traveled (s) for each of the two bodies, simply apply the equation :