A stone whirled at the end of a rope 25cm long make 5 complete revolution in 3 seconds. Find the angular velocity.
Circumference = pi * Dia. = 3.14 * 50 = 157 cm.
Va = 5rev/3s * 6.28rad/rev = rad/s.
Note: The circumference was not required.
To find the angular velocity, we need to calculate the amount of radians covered per unit time.
First, let's determine the total angle covered by the stone in 5 complete revolutions. Since one revolution is equivalent to 2π radians, five complete revolutions would be 5 * 2π = 10π radians.
Next, we need to determine the time taken to cover this angle. We know that the time taken is 3 seconds.
Finally, we can calculate the angular velocity. The formula for angular velocity (ω) is given by ω = θ / t, where θ is the angle covered and t is the time taken.
Substituting the values, we get ω = 10π radians / 3 seconds.
Hence, the angular velocity of the stone is 10π / 3 radians per second, or approximately 10.47 radians per second.