Understanding Inertia and the Parallel Axis Theorem

The video tutorial explains the concept of inertia and how to calculate it for different systems. It starts with two 10 kg blocks and discusses the effect of changing the axis of rotation. The parallel axis theorem is introduced to calculate new inertia values. The tutorial then provides an example with four masses and concludes with the inertia of a thin rod, demonstrating the use of the parallel axis theorem.

What is the total inertia of a system with two 10 kg blocks separated by 10 meters when the axis of rotation is at the center of mass?

• 750 kg·m²

• 1000 kg·m²

• 500 kg·m²

• 250 kg·m²

How does the inertia change when the axis of rotation is moved to the center of one of the 10 kg masses?

• It becomes 750 kg·m²

• It increases to 1000 kg·m²

• It remains 500 kg·m²

• It decreases to 250 kg·m²

What is the inertia of a system with four 4 kg blocks when the axis of rotation passes through the center of mass?

• 100 kg·m²

• 200 kg·m²

• 300 kg·m²

• 400 kg·m²

When the axis of rotation is moved 9 meters to the left in the four-mass system, what is the new inertia?

• 1969 kg·m²

• 1696 kg·m²

• 1296 kg·m²

• 1600 kg·m²

Using the parallel axis theorem, what is the new inertia of the four-mass system when the axis is moved?

• 1296 kg·m²

• 1969 kg·m²

• 1600 kg·m²

• 1696 kg·m²

What is the formula for the inertia of a thin rod when the axis of rotation passes through its center?

• 1/2 ml²

• 1/4 ml²

• 1/12 ml²

• 1/3 ml²

How does the inertia of a thin rod change when the axis of rotation is moved to the edge?

• It remains 1/12 ml²

• It becomes 1/4 ml²

• It becomes 1/3 ml²

• It becomes 1/2 ml²

What is the displacement used in the parallel axis theorem for a rod when the axis is moved to the edge?

• 1/2 of the length

• 1/4 of the length

• 1/3 of the length

• The full length

What is the purpose of the parallel axis theorem?

• To find the center of mass

• To measure the distance between masses

• To calculate the mass of a system

• To determine the new inertia when the axis is shifted

What is the condition for using the parallel axis theorem?

• The masses must be different

• The new axis must be perpendicular to the original

• The original axis must pass through the center of mass

• The system must be asymmetrical