**Acceleration in Uniform Circular Motion**

In uniform circular motion, an object moves in a circular path at a constant speed. Even though the speed remains constant, the object is constantly changing its direction, which means it is experiencing acceleration. The acceleration in uniform circular motion is directed towards the center of the circle and is known as centripetal acceleration.

**Relationship between Frequency and Angular Velocity**

The frequency of an object in uniform circular motion refers to the number of complete revolutions it makes in a given time period. It is usually measured in hertz (Hz), which represents the number of cycles completed per second. The angular velocity, on the other hand, is a measure of how fast an object is rotating and is usually measured in radians per second (rad/s).

The relationship between frequency (f) and angular velocity (ω) is given by the equation:

ω = 2πf

where ω is the angular velocity and 2π is the constant representing one complete revolution (2π radians).

**Effect of Doubling the Frequency**

When the frequency of an object in uniform circular motion is doubled, it means that the object completes twice as many revolutions in the same time period. Let's consider an object with an initial frequency f1 and angular velocity ω1. If the frequency is doubled to 2f1, the angular velocity would also double to 2ω1.

**Effect on Acceleration**

The centripetal acceleration (ac) of an object in uniform circular motion is given by the equation:

ac = ω^2r

where r is the radius of the circular path.

If the frequency is doubled, the angular velocity is also doubled. Substituting the new angular velocity (2ω1) into the equation for centripetal acceleration, we get:

ac = (2ω1)^2r
= 4ω1^2r

Therefore, when the frequency is doubled, the acceleration becomes four times its initial value. In other words, doubling the frequency results in a quadrupling of the acceleration.

This can be understood intuitively as the object is completing twice as many revolutions in the same time period. As a result, it is changing its direction more frequently, requiring a higher acceleration to maintain the circular motion.

In conclusion, when the frequency of an object in uniform circular motion is doubled, its acceleration becomes four times its initial value. This relationship can be explained by the equation for centripetal acceleration, which is dependent on the square of the angular velocity.