# Moments of Inertia Homework: Find Max Height H

• hold AP 2010
SirBouncyBall are discussing two different parts of a homework problem involving a block and a hoop, both sliding up an incline with an initial speed v0. The incline is on an angle, &theta;, and both objects stop sliding at some height H. The question asks for the max height H that the objects will reach if the incline is frictionless. One solution is given for the block, and another person suggests that the solution for the hoop would be the same. However, there may be some differences in the calculations because the block has mass distributed throughout its body, while the hoop's mass is concentrated at its edges.

## Homework Statement

part a) A block of mass m slides up an incline with an initial speed v0. The incline is on an angle,
Code:
&theta;
, and block stops sliding at height H.
-If the incline is frictionless, determine the max height H to which the block will rise, in terms of given quantities and appropriate constants.

part b) A thin hoop of mass m and radius R slides up an incline with an initial speed v0. The incline is on an angle,
Code:
&theta;
, and block stops sliding at height H.
-If the incline is frictionless, determine the max height H to which the hoop will rise, in terms of H and the given quantities.

## Homework Equations

thin hoop I = MR2

## The Attempt at a Solution

part a)

mgH = 1/2 mv02
therefore, H = (1/2)(v02/g)

& wouldn't part b be the same answer? or am I missing something mathematically?

hold AP 2010 said:
wouldn't part b be the same answer? or am I missing something mathematically?
I agree, it should be the same. It has nothing to do with the moment of inertia of the hoop if the hoop is sliding. The centre of mass is what you have to measure the height from.

AM

## 1. What is a moment of inertia?

A moment of inertia is a measure of an object's resistance to changes in rotational motion. It is calculated by summing the mass of each particle in the object multiplied by the square of its distance from the axis of rotation.

## 2. How do I calculate the moment of inertia for a given object?

The moment of inertia for a given object can be calculated using the formula I = ∑mr², where I is the moment of inertia, m is the mass of each particle, and r is the distance from the axis of rotation. You may also need to use different formulas for different shapes, such as the moment of inertia for a rod or a cylinder.

## 3. What is the purpose of finding the maximum height in moments of inertia homework?

The maximum height in moments of inertia homework is often used to determine the stability of an object or the maximum potential energy it can possess at a given point. It is an important concept in understanding rotational motion and can also be used to analyze the behavior of various mechanical systems.

## 4. How do I find the maximum height using moments of inertia?

To find the maximum height, you can use the equation H = I/(mga), where H is the maximum height, I is the moment of inertia, m is the mass of the object, g is the acceleration due to gravity, and a is the angular acceleration. Alternatively, you can use conservation of energy principles to find the maximum height.

## 5. What are some real-life applications of moments of inertia?

Moments of inertia are used in various fields, such as physics, engineering, and robotics. They are essential in designing stable structures, understanding the behavior of rotating objects, and analyzing the motion of celestial bodies. They are also used in calculating the performance of vehicles, such as cars and airplanes, and in designing gyroscopes and other mechanical systems.