Calculating Inertia and Radius of Gyration for a Rolling Object

In summary, planar motion of a rigid body is the movement of a solid object in a two-dimensional plane, with three types of motion: translational, rotational, and general planar. A rigid body maintains its shape and size, while a non-rigid body can deform. The moment of inertia is a measure of resistance to rotational motion, and in planar motion of a rigid body, angular momentum is conserved if no external torque or forces act on the system.
  • #1
shemy
5
0
Right,

I need to find out the Radius of gyration of an object as it rolls down a ramp...

So I've got the equation

K=r square root((g.t^2 sin theta/ 2x) -1))

These are the numbers I have...

Object A

R = 0.004
g = 9.81
t = 16.45
theta = 5.31
x = 0.66


I got an answer of 0.054

I think that's right however to work out inertia you use the equation

Iz = MR^2 / 2

Should that give you inertia? I got an answer of 0.136

I don't if that answers still for K and I need to work out inertia still?

Cheers

Shemy
 
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  • #2
Anyone?
 

FAQ: Calculating Inertia and Radius of Gyration for a Rolling Object

What is planar motion of a rigid body?

Planar motion of a rigid body refers to the movement of a solid object in a two-dimensional plane, where all points of the object move in parallel planes and maintain a fixed distance from each other.

What are the three types of planar motion?

The three types of planar motion are translational motion, rotational motion, and general planar motion. Translational motion involves movement in a straight line, rotational motion involves movement around an axis, and general planar motion involves a combination of both.

What is the difference between a rigid body and a non-rigid body?

A rigid body is a solid object that maintains its shape and size even when subjected to external forces. In contrast, a non-rigid body is one that can deform or change shape under external forces.

What is the moment of inertia in planar motion of a rigid body?

The moment of inertia is a measure of an object's resistance to changes in rotational motion. In planar motion of a rigid body, it is the sum of the products of each particle's mass and its distance from the axis of rotation squared.

How is angular momentum conserved in planar motion of a rigid body?

In planar motion of a rigid body, angular momentum is conserved if there are no external torque or net external forces acting on the system. This means that the total angular momentum of the system remains constant throughout the motion.

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