Uniform Circular Motion

In this lesson .. let me help go through circular Motion and its importance along with sample problem.
The revolution of moon around the Earth and the revolution of an artificial satellite in a circular orbit round the Earth are examples of circular motion.
Consider a particle moving with constant speed along the circumference of a circle of radius R in the anticlockwise direction. The time taken by the particle to go round the circle once is called the time period of the particle and is denoted by the letter T.
Examples on Uniform Circular Motion -
Below are the following examples on uniform Circular Motion.
Example 1 - Twirling an object tied to a rope in a horizontal circle. (Note that the object travels in a horizontal circle, but the rope itself is not horizontal). If the tension in the rope is 100 N, the object's mass is 3.7 kg, and the rope is 1.4 m long, what is the angle of the rope with respect to the horizontal, and what is the speed of the object?

As always, the place to start is with a free-body diagram, which just has two forces, the tension and the weight. It's simplest to choose a coordinate system that is horizontal and vertical, because the centripetal acceleration will be horizontal, and there is no vertical acceleration.

The tension, T, gets split into horizontal and vertical components. We don't know the angle, but that's OK because we can solve for it. Adding forces in the y direction gives:

This can be solved to get the angle:

In the x direction there's just the one force, the horizontal component of the tension, which we'll set equal to the mass times the centripetal acceleration:

We know mass and tension and the angle, but we have to be careful with r, because it is not simply the length of the rope. It is the horizontal component of the 1.4 m (let's call this L, for length), so there's a factor of the cosine coming in to the r as well.

Rearranging this to solve for the speed gives:

which gives a speed of v = 5.73 m/s.

I hope example was more explanatory and easy to understandable as well. Did you enjoy reading this and was it really helpful do you?.. Do you still require more help on Physics like this... Don't worry.. i can help you on like this... keep reading and may be in the next lesson let us learn on Graphical Representation of Uniform Motion.