Solving Rotational Problem: Conserving Momentum, Energy & Mass

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In summary, the problem involves a stick of length L and mass M on a frictionless surface, colliding with a ball of mass m and speed v at a distance d below its centre. The collision is elastic, meaning that there is no loss of kinetic energy. The quantities conserved in this collision are linear momentum and angular momentum, and the mass of the ball must be such that it remains at rest immediately after the collision.
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iitjee10
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Homework Statement


A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in anyway.
A ball of mass m moving with speed v collides elastically with the stick at a distance d below its centre.
(a) Which quantities are conserved in this collision?
(b) What must be the mass of the ball so that it remains at rest immediately after collision?



Homework Equations





The Attempt at a Solution


Here if we conserve linear momentum,
we get mv=Mv1 (As the ball remains at rest.)
But I don't think this is right because if we conserve angular momentum, then we get something else, and if we conserve kinetic energy, then we get something else.
So fow do i go about this question?
 
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  • #2
Hi iitjee10! :smile:

i] in any collision (with no external forces), both momentum and angular momentum are always conserved

ii] what does "elastically" mean?
 
  • #3
ii] what does "elastically" mean?
It means they collide with no loss of kinetic energy. :wink:
 
  • #4
elastically means coefficient of restitution is 1
 

1. What is rotational motion and why is it important to solve rotational problems?

Rotational motion refers to the movement of an object around an axis or center point. It is important to solve rotational problems because many real-world scenarios involve rotational motion, such as the movement of planets around the sun or the spinning of a wheel. Solving rotational problems allows us to understand and predict the behavior of objects in motion.

2. What is the principle of conservation of momentum and how does it apply to rotational problems?

The principle of conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on it. In rotational problems, this means that the total angular momentum of a system will remain constant unless an external torque is applied. This allows us to use the principle to solve for unknown quantities, such as the angular velocity or moment of inertia of an object.

3. How does energy conservation apply to rotational problems?

Energy conservation applies to rotational problems because rotational motion involves the transfer of energy between potential and kinetic forms. In a closed system, the total energy remains constant, meaning that the sum of the kinetic and potential energies will remain constant throughout the motion. This allows us to use the principle of conservation of energy to solve for unknown quantities, such as the angular velocity or torque of an object.

4. What is the role of mass in solving rotational problems?

Mass plays a crucial role in rotational problems because it affects an object's moment of inertia, which is a measure of its resistance to rotational motion. The greater an object's mass and distribution of mass around its axis of rotation, the greater its moment of inertia will be. This means that objects with larger moments of inertia will require more torque to rotate at the same angular velocity as objects with smaller moments of inertia.

5. What are some common techniques for solving rotational problems?

Some common techniques for solving rotational problems include using the equations for rotational motion, applying the principles of conservation of momentum and energy, and using the concept of torque. Other techniques may involve breaking the problem down into smaller parts or using diagrams and free-body diagrams to visualize the problem. Additionally, using the correct units and converting between linear and angular quantities can also be helpful in solving rotational problems.

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