A stone is thrown in a circular path with a radius of 3 m. If the stone complete

A stone is thrown in a circular path with a radius of 3 m. If the stone completes 4 revolutions in 8 seconds, what is the angular speed?

A stone is thrown in a circular path with a radius of 3 m. If the stone completes 4 revolutions in 8 seconds, what is the angular speed?

Step 1: Understand that a stone is thrown in a circular path with a radius of 3 m.
Step 2: Know that one complete revolution around a circle is equal to 2π radians.
Step 3: Since the stone completes 4 revolutions, calculate the total angle in radians: 4 revolutions * 2π radians/revolution = 8π radians.
Step 4: The time taken for these 4 revolutions is given as 8 seconds.
Step 5: To find the angular speed (ω), use the formula: Angular speed (ω) = Total angle / Time.
Step 6: Substitute the values into the formula: ω = (8π radians) / (8 seconds).
Step 7: Simplify the equation: ω = π radians/second.

Angular Speed – Angular speed is the rate of change of angular displacement and is calculated as the total angle covered divided by the time taken.
Revolutions to Radians Conversion – Understanding that one complete revolution corresponds to an angle of 2π radians is crucial for converting revolutions to radians.
Time Calculation – The time taken for the revolutions is essential for calculating angular speed, emphasizing the relationship between time and angular displacement.