02:08
Habib
The importance of Definite integrals is that they help find the area between the two limits of any graph. For example, let's take a look at this velocity-time graph:
Friday, 10 February 2012
Wednesday, 8 February 2012
Physics: Rigid Body Dynamics #2: Angular momentum and its conservation
Angular expressions, as mentioned before, can be derived from linear expressions by replacing some values:
Tuesday, 7 February 2012
Physics: Rigid Body Dynamics #2: Conservation of energy
Law of conservation of energy: {Energy cannot be created nor destroyed. It can only change from one form to another}. As this law states, a system's Total energy will never change. However, it might gain a certain type of energy, and lose another simultaneously. Example:
This object has potential energy, which means the stored energy in it. It has potential energy because if the surface below it was removed, it will fall down, and thus gain kinetic energy. However, it will rotate around its own axis as well, thus gaining both linear and rotational kinetic energy:
Monday, 6 February 2012
Math: Primitive Functions
Primitive Functions are important in calculus, because they are the main concept behind integration (Reverse Differentiation). To differentiate an expression, the power of x is reduced by one and multiplied by its coefficient. Example:
Sunday, 5 February 2012
Physics: Rigid Body Dynamics #1: Rotational Kinetic Energy
In linear motion, there is an expression know as kinetic energy (KE). This isn't actually kinetic energy in genral, but it was linear kinetic energy. In circular motion, there is an expression known as Rotational
Kinetic energy kinetic energy. The concept behind Rotational kinetic energy is similar to linear kinetic energy. However, both are not interchangable.
Friday, 3 February 2012
Physics: Rigid Body Dynamics #1: Centripetal acceleration and moment of inertia
In Rigid Body Statics, the sum of all torques and forces was zero. This meant that both linear acceleration and centripetal acceleration are equal to zero, and thus we were not concerned with them:
In Rigid Body Dynamics, however, there is a Torque. Thus, an expression relating torque with centripetal acceleration must be derived:
This is the main idea behind Rigid Body Dynamics.
In Rigid Body Dynamics, however, there is a Torque. Thus, an expression relating torque with centripetal acceleration must be derived:
This is the main idea behind Rigid Body Dynamics.
Brainteaser #1: "Secret Password"
Michael wants to get in the math genius club. There is a man guarding the place of the club. Michael hides in the bushes with the hopes of someone from the club to come and give the password to the guard. A man with the suit case appears the guard asks him: “Two plus two?” The man answers: “Three”. The guard lets him in. Michael gets confused. A few minutes later, a lady with a laptop appears. The guard asks her: “seven goes into forty nine how many times?” She answers: “Eight”. The guard lets her in. Michael gets even more confused. Finally, a kid with glasses appears. The guard asks him: “What is twenty one times two?” The kid answers: “Six”. The guard lets him in. Michael decides to take a shot, so he goes to the guard, and the guard asks him: “Five Squared?” Michael answers: “Twenty Five!” The guard shouts at him, and asks him to never show up. What answer should Michael have given to the guard, in order to get into the club?
