Consider an object rotating at a velocity V with a mass a certain distance away R. When the distance R is reduced by half, the velocity is doubled. Briefly explain why this happens.
When an object is in rotation, it has an angular momentum. The laws of motion state that momentum must be conserved, so if the radius of the mass is halved, the velocity must double in order to keep the conservation of momentum.
Briefly explain the VESPR Theory of Atoms and the VESPR numbers.
The VESPR Theory is a model used to explain the geometry of atoms and molecules based on the number of electrons surrounding the central atoms. VESPR numbers represent the hybridization of electron orbitals of an atom. For example, in water, Oxygen as the central atom has two sigma bonds and two lone pairs of electrons, meaning it has a VESPR number of 4, so it is an sp3 hybridized atom.
Briefly explain the Product and Quotient Rules for derivatives.
Let F and G represent two functions, and F' and G' represent their derivatives. The Product Rule states that If two functions are being multiplied together, F*G, the derivative is equal to F*G' + G*F'. The Quotient rule states that if two functions are being divided, F/G, the derivative is equal to (G*F' - F*G')/G^2.