A particle completes 4 revolution per second on a circular path of radius 0.25m. Calculate the angular velocity of partical

Va = 4rev/s * 6.28rad/rev = 25.12 Rad/s.

angular velocity is in ... radians per second ... rad/s

there are 2π radians in one revolution

for angular velocity, the length of the radius is immaterial

The angular velocity, denoted by ω (omega), is a measure of how quickly an object is rotating. It is defined as the angle turned per unit of time.

In this case, the particle completes 4 revolutions in 1 second.

To find the angular velocity, we need to convert revolutions per second to radians per second, as radians are the standard unit for measuring angles in physics.

One revolution is equal to 2π radians, so 4 revolutions would be 4 * 2π radians.

Therefore, the angular velocity is:

ω = (4 * 2π) radians / 1 second
= 8π radians / 1 second

The angular velocity of the particle is 8π radians per second.

To calculate the angular velocity of a particle moving in circular motion, you can use the formula:

Angular velocity (ω) = 2πf

Where:
- ω represents the angular velocity
- π (pi) is a mathematical constant approximately equal to 3.14159
- f is the frequency of the particle's circular motion.

In this case, the frequency is given as 4 revolutions per second. However, we need to convert revolutions into cycles or hertz (Hz), which represents the number of complete cycles per second.

Since 1 revolution is equal to 1 cycle, the frequency in hertz is also 4 Hz.

Now, we can substitute the value into the formula:

ω = 2π(4 Hz) = 8π Hz

Therefore, the angular velocity of the particle is 8π radians per second.