Lecture 25 - Center of Mass

What is the center of mass (cm) in a system?

The center of mass is a special point in space representing the average position of all the particles in a system, allowing it to be treated as a single point object.

How is the center of mass calculated for a system of multiple masses?

The center of mass is calculated using the formula: r_cm = (m1r1 + m2r2 + ... + mn*rn) / (m1 + m2 + ... + mn).

For geometrically symmetrical objects with uniform density, where is the center of mass located?

The center of mass is located at the geometric center of the object.

What happens to the total momentum of a system when external forces are absent?

The total momentum remains constant, and the velocity of the center of mass does not change.

What is the formula for calculating the x-coordinate of the center of mass in 2D?

The formula is: x_cm = (m1x1 + m2x2 + ... + mn*xn) / (m1 + m2 + ... + mn).

In the example of James and Ramon, what remains constant when they pull on the rope?

The position of the center of mass remains constant because no external forces are acting on the system.

What is the significance of Newton's 3rd Law in determining motion within a system?

Internal forces cancel each other out, so only external forces affect the motion of the center of mass.

How is the acceleration of the center of mass determined when a force is applied?

The acceleration of the center of mass can be calculated using the formula: a_cm = F_ext / M, where M is the total mass of the system.

What is the relationship between impulse and change in momentum?

Impulse is equal to the change in momentum: J = F * Δt = Δp.

What does it mean for objects to be treated as point particles in physics?

It means we can simplify the analysis by focusing on their center of mass and their motion as if all mass is concentrated at that point.