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What is the effect of increasing the distance of mass from the axis of rotation?

Increases the rotational inertia.

What is the effect of increasing the mass of an object on its rotational inertia?

Increases the rotational inertia.

What happens if a rigid body rotates about its center of mass?

The rotational inertia is minimized.

What is the effect of applying a torque to an object with a high rotational inertia?

The object will experience a smaller angular acceleration.

What happens if the axis of rotation is shifted away from the center of mass?

The rotational inertia increases, as described by the parallel axis theorem.

How do you calculate the total rotational inertia of multiple objects?

Sum the individual rotational inertias: $\I_{\text{tot}} = \sum I_i = \sum m_i r_i^2$

Outline the steps to find rotational inertia of a solid object.

Imagine the solid is made of tiny masses dm. 2. Use the integral: $I = \int r^2 dm$ . 3. Integrate over the entire object.

What are the steps to apply the parallel axis theorem?

Identify the axis of rotation. 2. Find the rotational inertia about the center of mass ( $I_{cm}$ ). 3. Determine the distance d between the axes. 4. Calculate $I' = I_{cm} + Md^2$ .

Describe the process of deriving rotational inertia using calculus.

Define a mass element dm. 2. Express dm in terms of spatial variables. 3. Determine the limits of integration. 4. Evaluate the integral $I = \int r^2 dm$ .

How do you calculate rotational inertia for a system of discrete particles?

Identify each particle's mass ( $m_i$ ) and distance ( $r_i$ ) from the axis of rotation. 2. Calculate each particle's rotational inertia ( $I_i = m_i r_i^2$ ). 3. Sum the individual rotational inertias: $I_{tot} = \sum I_i$ .

How do you calculate the total rotational inertia for multiple objects?

Calculate the rotational inertia ( $I = mr^2$ ) for each object and then sum them: $I_{tot} = \sum I = \sum mr^2$ .

What are the steps to apply the parallel axis theorem?

Identify $I_{cm}$ (inertia about the center of mass). 2. Determine 'd' (distance between the parallel axis and the center of mass axis). 3. Calculate $I' = I_{cm} + Md^2$ .

All Flashcards

What is the effect of increasing the distance of mass from the axis of rotation?

Increases the rotational inertia.

What is the effect of increasing the mass of an object on its rotational inertia?

Increases the rotational inertia.

What happens if a rigid body rotates about its center of mass?

The rotational inertia is minimized.

What is the effect of applying a torque to an object with a high rotational inertia?

The object will experience a smaller angular acceleration.

What happens if the axis of rotation is shifted away from the center of mass?

The rotational inertia increases, as described by the parallel axis theorem.

How do you calculate the total rotational inertia of multiple objects?

Sum the individual rotational inertias: $\I_{\text{tot}} = \sum I_i = \sum m_i r_i^2$

Outline the steps to find rotational inertia of a solid object.

Imagine the solid is made of tiny masses dm. 2. Use the integral: $I = \int r^2 dm$ . 3. Integrate over the entire object.

What are the steps to apply the parallel axis theorem?

Identify the axis of rotation. 2. Find the rotational inertia about the center of mass ( $I_{cm}$ ). 3. Determine the distance d between the axes. 4. Calculate $I' = I_{cm} + Md^2$ .

Describe the process of deriving rotational inertia using calculus.

Define a mass element dm. 2. Express dm in terms of spatial variables. 3. Determine the limits of integration. 4. Evaluate the integral $I = \int r^2 dm$ .

How do you calculate rotational inertia for a system of discrete particles?

Identify each particle's mass ( $m_i$ ) and distance ( $r_i$ ) from the axis of rotation. 2. Calculate each particle's rotational inertia ( $I_i = m_i r_i^2$ ). 3. Sum the individual rotational inertias: $I_{tot} = \sum I_i$ .

How do you calculate the total rotational inertia for multiple objects?

Calculate the rotational inertia ( $I = mr^2$ ) for each object and then sum them: $I_{tot} = \sum I = \sum mr^2$ .

What are the steps to apply the parallel axis theorem?

Identify $I_{cm}$ (inertia about the center of mass). 2. Determine 'd' (distance between the parallel axis and the center of mass axis). 3. Calculate $I' = I_{cm} + Md^2$ .