b.) Your friend Bob proposes that you can do this calculation more easily. He condenses the entire ice cream cone into a point mass located at the its center of mass, then uses the point mass formula (I=mr2). What would be the distance "r" that he would use, and the rotational inertia that would result from his calculation? r = X m I = X kg-m2 Is Bob's method correct? no; you need to use the object's exact shape in your "I" calculations

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**The Ice Cream Cone Model**

The ice cream cone depicted can be analyzed through two geometric approximations:

- **Scoop on Top**: This can be modeled as a uniform solid sphere with a mass \( M_1 = 0.027 \, \text{kg} \) and a radius \( R_1 = 0.03 \, \text{m} \).

- **Waffle Cone Base**: This is approximated as a cylinder, with a mass \( M_2 = 0.038 \, \text{kg} \) and a radius \( R_2 = 0.01 \, \text{m} \). The cylinder is uniform and solid, assuming it is filled with ice cream.

**Diagram Explanation**

- The illustration shows a blue ice cream scoop on top of a waffle cone.
- Arrows indicate rotational movement around the axis of both the sphere and the cylinder.
- The labels \( M_1 \) and \( M_2 \) denote the masses of the sphere and cylinder, respectively.
- Lines indicate the radii \( R_1 \) of the sphere and \( R_2 \) of the cylinder.
Transcribed Image Text:**The Ice Cream Cone Model** The ice cream cone depicted can be analyzed through two geometric approximations: - **Scoop on Top**: This can be modeled as a uniform solid sphere with a mass \( M_1 = 0.027 \, \text{kg} \) and a radius \( R_1 = 0.03 \, \text{m} \). - **Waffle Cone Base**: This is approximated as a cylinder, with a mass \( M_2 = 0.038 \, \text{kg} \) and a radius \( R_2 = 0.01 \, \text{m} \). The cylinder is uniform and solid, assuming it is filled with ice cream. **Diagram Explanation** - The illustration shows a blue ice cream scoop on top of a waffle cone. - Arrows indicate rotational movement around the axis of both the sphere and the cylinder. - The labels \( M_1 \) and \( M_2 \) denote the masses of the sphere and cylinder, respectively. - Lines indicate the radii \( R_1 \) of the sphere and \( R_2 \) of the cylinder.
**Problem Statement:**

Your friend Bob proposes that you can do this calculation more easily. He condenses the entire ice cream cone into a point mass located at its center of mass, then uses the point mass formula \(I = mr^2\).

**Question:**

What would be the distance "r" that he would use, and the rotational inertia that would result from his calculation?

- \(r = \_\_\_\_\) m ✖️
- \(I = \_\_\_\_\) kg·m² ✖️

Is Bob's method correct?
- No; you need to use the object's exact shape in your "I" calculations ✔️
Transcribed Image Text:**Problem Statement:** Your friend Bob proposes that you can do this calculation more easily. He condenses the entire ice cream cone into a point mass located at its center of mass, then uses the point mass formula \(I = mr^2\). **Question:** What would be the distance "r" that he would use, and the rotational inertia that would result from his calculation? - \(r = \_\_\_\_\) m ✖️ - \(I = \_\_\_\_\) kg·m² ✖️ Is Bob's method correct? - No; you need to use the object's exact shape in your "I" calculations ✔️
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