The ice cream cone shown below can be approximated as follows: · scoop on top = uniform solid sphere (M1 = 0.027 kg and R1 = 0.03 m) • waffle cone base= cylinder (M2 = 0.038 kg and R2 = 0.01 m), which is uniform and solid also (it's filled with ice cream!) M, R, R2 M, If this entire ice cream cone were to be rotated about the axis shown, Rotational Inertia: a.) What would the the rotational inertia (I) of: Scoop on top: I1 = kg-m2 cone base: I2 = kg-m2 the whole ice cream cone: Itot = kg-m2 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? m
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![**Problem Statement:**
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 its center of mass, then uses the point mass formula \( I = mr^2 \).
**Tasks:**
1. Determine the distance "r" that Bob would use.
2. Calculate the rotational inertia that would result from his calculation.
**Inputs:**
- Distance \( r \) = ______ m
- Rotational Inertia \( I \) = ______ kg·m\(^2\)
**Question:**
Is Bob's method correct?
- [ ] ---Select---
- [ ] yes; this is much easier--thanks Bob!
- [ ] no; you need to use the object's exact shape in your "I" calculations
---
**Instructions for Input:**
- Input the appropriate value for distance \( r \) in meters, considering the center of mass.
- Calculate and input the rotational inertia \( I \) in kg·m\(^2\) based on Bob’s simplification.
- Select the appropriate response regarding the correctness of Bob's method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F053de147-f729-43a3-9862-d1dda037cfcc%2F0322c072-43cb-4ae7-883c-d883c5d8620c%2Ferlca7l_processed.png&w=3840&q=75)
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