Derivation of Pendulum equations method 2

The video tutorial explains how to calculate the equations of motion for a pendulum using rotational kinetic energy. It begins by introducing the pendulum system and the assumptions made, such as neglecting friction and considering the mass of the cord as zero. The tutorial then delves into the concepts of mechanical energy, rotational kinetic energy, and moment of inertia. Using trigonometry and calculus, the instructor derives the equation of motion, ultimately showing that the angular acceleration is proportional to the negative sine of the angle. The video concludes by summarizing the approach and confirming that the same result can be obtained by considering linear velocity.

What is the main difference in approach between this problem and the previous one discussed by the teacher?

• Including air resistance in the calculations

• Using linear kinetic energy instead of rotational kinetic energy

• Considering friction in the system

• Using rotational kinetic energy instead of linear kinetic energy

What does the constant K represent in the energy equation?

• The work done by non-conservative forces

• The kinetic energy of the system

• The potential energy of the system

• The total mechanical energy of the system

What assumption is made about the forces acting at the hinge of the pendulum?

• The normal force does work

• The normal force is zero

• The normal force does no work

• The normal force is constant

Why is the term for linear kinetic energy not included in the energy equation?

• The mass is not rotating

• The pivot point is moving

• The rope is elastic

• The pivot point is stationary

How is the moment of inertia for the pendulum system calculated?

• By using the linear velocity of the mass

• By considering the elasticity of the rope

• By summing the squares of the distances of discrete masses from the pivot point

• By considering the mass of the rope

What trigonometric function is used to express the vertical distance in the pendulum system?

• Cosine

• Secant

• Tangent

• Sine

What is the final form of the equation of motion derived for the pendulum?

• Theta double dot equals negative L over G times sine Theta

• Theta double dot equals L over G times sine Theta

• Theta double dot equals negative G over L times sine Theta

• Theta double dot equals G over L times sine Theta