Table of Contents
- 1 Why does a hollow cylinder have a greater moment of inertia?
- 2 Which has more moment of inertia hollow sphere or solid sphere?
- 3 When a wheel rolls without slipping its motion is a combination of rotational and translational motion?
- 4 Why does a solid disk have a greater moment of inertia than a solid sphere?
- 5 How does the cylinder roll without slipping down the incline?
- 6 What is the moment of inertia to plain acceleration?
Why does a hollow cylinder have a greater moment of inertia?
So if a hollow cylinder has same mass as that of a solid cylinder then we can conclude that the mass distribution of hollow cylinder is farther from the axis of cylinder as compared to a solid cylinder. This is why the moment of inertia of hollow cylinder is greater than that of solid cylinder.
What is the moment of inertia for a hollow cylinder?
HOLLOW CYLINDER MOMENT OF INERTIA
Moment of Inertia of Hollow Cylinder Formula | |
---|---|
Mass moment of inertia about x axis | Ix= (m/12) * (3*(R22+R12) + h2) |
Mass moment of inertia about y axis | Iy= (m/12) * (3*(R22+R12) + h2) |
Mass moment of inertia about z axis | Iz= (m/2) * (R12+R22) |
Which has more moment of inertia hollow sphere or solid sphere?
A hollow sphere will have a much larger moment of inertia than a uniform sphere of the same size and the same mass.
Which object has largest moment of inertia?
Masses that are further away form the axis of rotation have the greatest moment of inertia.
When a wheel rolls without slipping its motion is a combination of rotational and translational motion?
Rolling without slipping is a combination of translation and rotation where the point of contact is instantaneously at rest. The object will also move in a straight line in the absence of a net external force.
Why is moment of inertia of solid sphere less than hollow sphere?
But in case of a solid sphere, the same mass is distributed throughout at distance from zero to R from the axis of symmetry. Here, R is radius of cylinder/sphere. That is why a solid sphere has smaller moment of inertia than a hollow cylinder of same mass and radius.
Why does a solid disk have a greater moment of inertia than a solid sphere?
Based on the coefficients (2/5 and 1/2), the moment of inertia of solid disk is greater than the moment of inertia of a solid sphere. This phenomenon is caused by the difference in the distribution of mass around the axis.
How do you find the moment of inertia of a hollow cylinder?
The expression for the moment of inertiaof a hollow cylinderor hoop of finite thickness is obtained by the same process as that for a solid cylinder. The process involves adding up the moments of infinitesmally thin cylindrical shells.
How does the cylinder roll without slipping down the incline?
The cylinder rolls without slipping down the incline. Using the torque method about the center of mass, calculate the velocity of the center of mass of the cylinder when it reaches the bottom of the incline. 0, and it slides without rolling but due to friction it begins to roll until it rolls without slipping.
What are the moments of inertia for the limiting geometries?
The moments of inertia for the limiting geometries with this mass are: Ithin disk diameter= kg m2 Ithin rod end= kg m2 Show development of expressions Hollow cylinder case Index Moment of inertia concepts HyperPhysics*****Mechanics R Nave Go Back Moment of Inertia: Cylinder
What is the moment of inertia to plain acceleration?
It’s just like plain acceleration is to plain velocity. I like to call the moment of inertia the “rotational mass”. This is a property of a rigid object (with respect to some rotational axis) such that the greater the moment of inertia, the lower the angular acceleration (for a constant torque).