What are the steps to calculate the center of mass ( $x_{cm}$ ) along an axis for discrete objects?

Identify the mass ( $m_i$ ) and position ( $x_i$ ) of each object. 2. Calculate the sum of ( $m_i * x_i$ ) for all objects. 3. Calculate the sum of all masses ( $m_i$ ). 4. Divide the sum of ( $m_i * x_i$ ) by the sum of the masses.

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What are the steps to calculate the center of mass ( $x_{cm}$ ) along an axis for discrete objects?

Identify the mass ( $m_i$ ) and position ( $x_i$ ) of each object. 2. Calculate the sum of ( $m_i * x_i$ ) for all objects. 3. Calculate the sum of all masses ( $m_i$ ). 4. Divide the sum of ( $m_i * x_i$ ) by the sum of the masses.

What is the effect of applying an external force at the center of mass of a system?

The system will translate (move as a whole) in the direction of the applied force without rotation.

What is the effect of heating a solid system?

Heating a solid can change its structure.

What is the effect of a system rotating?

The center of mass will move in a straight line or remain stationary, while the system rotates around it.

What is the definition of 'center of mass'?

The average position of all the mass in a system.

Define 'system' in the context of physics.

A collection of objects whose interactions we are studying.

What are 'emergent properties'?

System properties that arise from the interactions of its parts.

What is macroscopic modeling?

Treating a system as a single object when internal details are unimportant.

Define 'lines of symmetry'.

Imaginary lines where if folded along it, the two halves of the object match exactly.