Moment of Inertia: Solid vs Hollow Disk on Incline

AI Thread Summary
A solid disk and a hollow disk of equal mass are compared in their descent down an incline. The moment of inertia plays a crucial role in determining which disk reaches the bottom first. The solid disk has a smaller moment of inertia because more of its mass is closer to the axis of rotation, while the hollow disk has a greater moment of inertia due to its mass being distributed further away. Consequently, the solid disk accelerates faster and will reach the bottom of the incline before the hollow disk. Understanding the relationship between mass distribution and moment of inertia is key to solving this problem.
Invictus1017
Messages
2
Reaction score
0

Homework Statement


Alright, so say I have a solid wood disk, and a hollowed out disk of equal mass.
I roll them both down an incline, which one gets to the bottom first and why?
The scenario is very similar to this:
http://youtube.com/watch?v=7mxV6f5nuJY



Homework Equations


I = MR ?




The Attempt at a Solution


Something do with moment of inertia i think.

Thanks alot.
 
Physics news on Phys.org
As you say, the moment of inertia is a crucial factor. You can answer this question quantitatively that is, explicitly calculate the moment of inertia for each disk and then evaluate it's acceleration. An alternative (and much easier) method would be to use the definition of Moment of Inertia for a point particle (I=mr2 not I=mr as you have above), and logical reasoning.

So to start we know that both their masses are equal, using the definition of I that I gave you above, can you make the next step?
 
Last edited:
I'm not sure but, the radius from the center of mass to the axis of the hollow disk is larger than the radius of the solid disk? Resulting in a smaller moment of inertia for the solid disk?
 
Last edited:
Invictus1017 said:
I'm not sure but, the radius from the center of mass to the axis of the hollow disk is larger than the radius of the solid disk? Resulting in a smaller moment of inertia for the solid disk?
Well you conclusion is correct, but your reasoning is wrong. The centre of mass of both disc both lie on the axis of rotation. However, the hollow disc has a greater proportion of its mass located further away from the axis of rotation, thus the moment of inertia is greater. Does that make sense?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Moment of inertia of a disk about an axis not passing through its CoM
Replies
11
Views
3K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
Replies
40
Views
5K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
Replies
8
Views
12K
What is the "r" in the moment of inertia?
Replies
13
Views
2K
Moment of Inertia of a hollow sphere with Mass 'M' and radius 'R'.
Replies
16
Views
4K
Rotational Inertia: Hoop vs Disk
Replies
19
Views
4K
Period of Pendulum: Spinning Disk Forces & Inertia Moment\
Replies
1
Views
1K
Moment of Inertia of an inclined disk
Replies
27
Views
5K
How Do You Calculate the Moment of Inertia for a Disk with a Central Hole?
Replies
2
Views
3K
Rolling 3 objects on an inclined plane
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top