Rotational energy convservation probelm, inertia

In summary, the problem involves shooting a small, solid, uniform ball from point P on a horizontal path, up a ramp, and onto a plateau. The ball then leaves the plateau and lands on a game board, 6cm from the right edge of the plateau. The vertical height from P to the top of the plateau is 5cm and the game board is 1.6cm down from the top of the plateau. Using conservation of energy, the required initial velocity at P can be calculated. However, rotational kinetic energy can be neglected since no information is provided about the ball's radius.
  • #1
Sonorus
2
0
A small, solid, uniform ball is to be shot up from point P so it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance (d=6cm) from the right edge of the plateau. The vertical height from P to the top of the plateau is 5 cm, and the game board is s 1.6 cm down from the top of the plateau. A MS paint diagram can be found here: http://imgur.com/rCCPq

Find the speed at witch the ball will be shot at P so it lands 6cm from the plateau.



Relevant equations:
Kinetic energy=.5(Inertia of center of mass)(angular velocity)^2+.5(mass)(velocity)^2
w=angular velocity
I=Inertia of center of mass



So, I've got the basic idea of the problem. I've found the required velocity as the ball leaves the plateau to land in the right spot with projectile motion. Now I'm supposed to use conservation of energy to find the initial velocity.

I don't know exactly how to proceed. The ball starts rotating immediately, so I'd have to include rotational kinetic energy in both in the energy at P, and at the top of the plateau, correct?

So does this look correct? I'm also not sure how to find the inertia used in these equations, so I'd appreciate help with that.

Energy@P= .5(mv^2) +.5(I)(w^2) (only kinetic energy)
Energy@plateu = .5(mv^2)+.5(I)(w^2)+mgy (kinetic energy +potential)
 
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  • #2
The reason the problem tells you it's a small ball is so you can neglect rotational energy. Even if you wanted to take rotational energy into account, you can't, because no information is provided about the ball's radius.
 
  • #3
Oh, huh. I guess that makes perfect sense, and makes the problem a lot easier. I wonder why it's in the back of the Rolling, Torque, and Angular Momentum chapter though, if it doesn't include any of those concepts.

Thanks for your help.
 

Related to Rotational energy convservation probelm, inertia

1. What is rotational energy conservation?

Rotational energy conservation is the principle that states that the total energy of a system remains constant in the absence of external torque. This means that the total amount of energy in a rotating object remains the same, even if the object changes its speed or direction of rotation.

2. How is rotational energy conserved?

Rotational energy is conserved because of inertia, which is the tendency of an object to resist changes in its state of motion. In a rotating object, the inertia of the object keeps it moving at a constant speed and direction, even in the presence of external forces.

3. What is inertia?

Inertia is a property of matter that describes an object's resistance to changes in its state of motion. The greater the inertia of an object, the more difficult it is to change its speed or direction of motion.

4. How does inertia affect rotational energy conservation?

Inertia is a key factor in rotational energy conservation because it is what allows an object to maintain its rotational motion without the need for continuous external forces. The greater the inertia of an object, the more difficult it is to change its rotational speed or direction.

5. What factors can affect rotational energy conservation?

There are several factors that can affect rotational energy conservation, including the mass and shape of the rotating object, the speed at which it is rotating, and any external forces acting on the object. Friction and air resistance can also play a role in affecting rotational energy conservation.

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