a wheel of radius R rotates making f revolutions per second. the quantity f is know as the frecuency of the motion. show tha 1/f is the time to complete one revolution, called the period T of the motion. show that the centripetal acceleration of a point at the rim of the wheel is a=4(3.14)^2Rf^2

3.14=pi

The distance around the wheel is 2PI*r

that is the distance it goes on one rev.

so on one rev, it goes 2PI*r, now in one second, it does this f times,

so the time for one revolution then is 1/f.

centripetal acceleration= v^2/r
but v= 2PI*r/period=2PI*r*f
v^2=4PI^2 r^2 f^2
so v^2/r= 4PI^2 f^2 r

To show that 1/f is the time to complete one revolution, called the period T of the motion, we can start by understanding the relationship between frequency and time.

Frequency (f) is the number of complete cycles or revolutions that occur in one second. In this case, f represents the number of revolutions per second made by the wheel.

If we want to find the time (T) it takes to complete one revolution, we need to find the reciprocal of the frequency. In other words, T = 1/f.

The reason for this is that when the frequency is f revolutions per second, it means that it takes 1/f seconds to complete one revolution. So, by taking the reciprocal of the frequency (1/f), we get the time to complete one revolution (T).

Now, let's move on to showing the centripetal acceleration of a point at the rim of the wheel.

Centripetal acceleration (a) is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle.

The formula for centripetal acceleration is given by a = (v^2) / r, where v is the linear velocity of the object and r is the radius of the circular path.

In this case, the linear velocity of the point at the rim of the wheel is given by the distance travelled per unit time, which is equal to the circumference of the wheel (2πR) multiplied by the frequency (f). So, v = 2πRf.

Substituting the value of v into the formula for centripetal acceleration, we get a = ((2πRf)^2) / R.

Simplifying this equation further, we have a = 4π^2Rf^2.

Now, you mentioned that 3.14 is equal to pi (π), so we can rewrite the equation as a = 4(3.14)^2Rf^2.

Therefore, the centripetal acceleration of a point at the rim of the wheel is given by a = 4(3.14)^2Rf^2.

I hope this explanation helps you understand how to derive the time to complete one revolution and the centripetal acceleration of a point at the rim of the wheel.