Moment of Inertia of Systems Video Lessons

Video Thumbnail

Example

Problem: Part A. What is a, the acceleration of the hoop’s center?Express your answer in terms of some of all of the variables m, θ, and g, the acceleration due to gravity.Part B. What is the minimum coefficient of static friction, µmin, needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, because the bottom point on the hoop is not moving relative to the ground (which is what it is meant by no slippage).Express your answer in terms of all of some of the variables m, r, and θ

FREE Expert Solution

The moment of inertia of a hoop about its center is:

Icm=mr2

Part A.

Let's consider the equation of motion along the x-axis:

mgsinθ - T = ma ..................... (1) where a is the acceleration down the incline. 

Rotational motion equation:

88% (163 ratings)
View Complete Written Solution
Problem Details

Part A. What is a, the acceleration of the hoop’s center?
Express your answer in terms of some of all of the variables m, θ, and g, the acceleration due to gravity.

Part B. What is the minimum coefficient of static friction, µmin, needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, because the bottom point on the hoop is not moving relative to the ground (which is what it is meant by no slippage).
Express your answer in terms of all of some of the variables m, r, and θ

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Moment of Inertia of Systems concept. You can view video lessons to learn Moment of Inertia of Systems. Or if you need more Moment of Inertia of Systems practice, you can also practice Moment of Inertia of Systems practice problems.