Conservation of energy in rotational motion

In summary, the conversation discusses a problem involving a uniform marble rolling down a symmetric bowl with different levels of friction on each side. The questions focus on the distance the marble travels and the role of friction in its motion. Energy equations are used to solve the problem, and it is determined that friction does not do work in this case since the marble is rolling without slipping.
  • #1
mit_hacker
92
0

Homework Statement


(Q) A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The left half of the bowl is rough enough to cause the marble to roll without slipping but the right half is frictionless.

(a) How far up the smooth side will the marble go, measured vertically from the bottom?

(b) How high up would the marble go if both sides were as rough as the left hand side?

(c) How do you account for the fact that the marble goes higher up with friction on the right side than without friction?



Homework Equations



KE = (1/2)MV^2 + (1/2)IcmW^2.
PE = mgh

The Attempt at a Solution



I am completely blank.
How do I account for the friction on just the right hand side?
Since the bowl is symmetrical, can I take its radius to be h?
Is it ok to say that the angular displacement of the marble is pi/2 from top to bottom?

Pleeeaseeeee help!:cry:
 
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  • #2
initial energy = mgh

bottom of the bowl, energy is (1/2)MV^2 + (1/2)IcmW^2.

relate W to V...

what do you get for V?

when it goes up the frictionless side what happens to the translational energy? what happens to the rotational energy?
 
  • #3
Friction?

What about friction? Don't we deduct that from the expression

(1/2)MV^2 + (1/2)IcmW^2 to get (1/2)MV^2 + (1/2)IcmW^2 -fD where f is force of friction?

Why don't we take that into account?
 
  • #4
mit_hacker said:
What about friction? Don't we deduct that from the expression

(1/2)MV^2 + (1/2)IcmW^2 to get (1/2)MV^2 + (1/2)IcmW^2 -fD where f is force of friction?

Why don't we take that into account?

friction only does work when the surfaces slide against each other... in this case it is rolling without any sliding... no energy is lost.

work by friction = frictional force*distance (this is the distance the point of application moves... but in this case there is no slipping, the point of application doesn't move at all... distance = 0).
 
  • #5
Thanks!

Hey, thanks a ton for that! I never knew that in rolling, friction does not do any work. Again, thanks a ton!:biggrin:
 
  • #6
mit_hacker said:
Hey, thanks a ton for that! I never knew that in rolling, friction does not do any work. Again, thanks a ton!:biggrin:

no prob. :)
 

FAQ: Conservation of energy in rotational motion

What is conservation of energy in rotational motion?

Conservation of energy in rotational motion is a fundamental principle in physics that states that energy cannot be created or destroyed, but can only be transferred or transformed. In rotational motion, this means that the total mechanical energy (kinetic and potential) of a system remains constant as long as there are no external forces acting on it.

How is rotational kinetic energy calculated?

Rotational kinetic energy is calculated using the formula E = 1/2 * I * ω^2, where E is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. Moment of inertia is a measure of an object's resistance to changes in its rotational motion, and is dependent on the mass and distribution of the object's mass. Angular velocity is the rate at which the object is rotating.

What is the relationship between rotational and translational kinetic energy?

Rotational and translational kinetic energy are both forms of kinetic energy, but they represent different types of motion. Translational kinetic energy is associated with the linear motion of an object, while rotational kinetic energy is associated with the rotational motion of an object about an axis. In some cases, these two forms of energy can be converted into one another, such as in the case of a rolling ball.

How is gravitational potential energy related to rotational motion?

Gravitational potential energy is a form of potential energy that is associated with an object's position in a gravitational field. In rotational motion, gravitational potential energy can be converted into rotational kinetic energy and vice versa. For example, a pendulum swinging back and forth converts its gravitational potential energy into rotational kinetic energy and back again as it swings.

What are some real-world applications of conservation of energy in rotational motion?

Conservation of energy in rotational motion is an important concept in many fields, including engineering, physics, and sports. Some examples of its real-world applications include calculating the energy required to launch a satellite into orbit, designing efficient wind turbines, and understanding the mechanics of a spinning top or gyroscope. It also plays a role in activities such as figure skating, gymnastics, and skateboarding, where rotational motion and conservation of energy are crucial for achieving certain moves and tricks.

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