An air craft makes a turn in a horizontal circle of radius100m. It is travelling with a velocity of 250m/sec. The angular velocity of the air craft will be?
Answer: 2.5 rad/sec
Explanation
Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t). It can be calculated using the formula:
ω = v / r
Where:
v = linear velocity (in m/s)
r = radius of the circle (in m)
Given:
v = 250 m/s (linear velocity)
r = 100 m (radius of the circle)
ω = v / r
= 250 m/s / 100 m
= 2.5 rad/s
So, the angular velocity of the aircraft is 2.5 rad/sec.