Rotation: Calculating Rotational Energy of Sphere with Steiner

  • Thread starter Thread starter Kruger
  • Start date Start date
  • Tags Tags
    Rotation
AI Thread Summary
To calculate the rotational energy of a sphere rolling down a frictionless plane, the moment of inertia is given as I = 2/5*m*r^2. The formula for rotational energy is Erot = 1/2*I*w^2, where w is the angular velocity. The confusion arises regarding the application of Steiner's theorem, which is used to find the moment of inertia about an axis parallel to one through the center of mass. Generally, Steiner's theorem is applied when the axis of rotation is not through the center of mass, but for a sphere rolling without slipping, it is not necessary. Understanding when to apply Steiner's theorem is crucial for solving problems involving rolling objects.
Kruger
Messages
213
Reaction score
0

Homework Statement



Consider a spere with momenta of inertia of 2/5*m*r^2 that rolls down a plane surface (no friction). I want to calculate the rotational energy of the sphere when it has speed v0.

Homework Equations



Erot=1/2*I*w^2

The Attempt at a Solution



My only problem is: Do I need to transform my I=2/5*m*r^2 with the rule of steiner, or don't I have to use the rule of Steiner? I would say no.
 
Physics news on Phys.org
I'm so confused because sometimes Steiner's theorem isn't used and sometimes it is used for rolling objects. Can you please generalize, when I have to use Steiner's theorem for rolling objects? Would be really helpful.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Similar threads

Two objects joined by a rectilinear cable rotating
Replies
8
Views
901
Calculate the magnetic moment of a rotating sphere
Replies
17
Views
2K
Motion of Sphere Rolling Down Rotating Cone
Replies
9
Views
2K
B What is the total kinetic energy of the Earth relative to the Sun?
Replies
40
Views
4K
Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
Earth's rotation slows down slightly over time -- How much energy is lost?
Replies
15
Views
2K
Question about springs and rotational/translational energy
Replies
4
Views
1K
Parallel Axis Theorem Not Working
Replies
28
Views
1K
Solve Steiner's Theorem Homework: 2 Thin Bars of Mass M, Length L
Replies
11
Views
2K
Minimal rotational kinetic energy for a gyroscope to precess
Replies
33
Views
3K

Hot Threads

Recent Insights

Back
Top