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Mechanics Big Mind Map, CHAPTER 8(RIGID BODIES), Free Fall :apple:,…

- - - - measure of the force that keeps a stationary object stationary, or a moving object moving at its current speed
      - The larger the inertia, the greater the force that is required to bring some change in its velocity in a given amount of time
      - depend on the mass
    - - describes how easily a body can be rotated about a given axis
        
        The larger the moment of inertia, the greater the amount of torque that will be required to bring the same change in its angular velocity in a given amount of time
        
        depends on the mass and also the distribution of mass
        
        if the mass distributed away from central axis of rotation, the inertia of object increase
        
        to rotate an object about different axes with an equal angular acceleration, different torque (or effort) is required
      - General equation, I = MR^2
  - - - net torque, τ = I α
  - - - Fnett = 0 or Fx = 0, Fy = 0, Fz = 0
        
        τ nett = 0 or τ x =0, τ y = 0, τ y = 0, τ z = 0
  - - - L = I w
- - - - equilibrium condition for forces, which we encountered when studying applications of Newton’s laws.
        
        F = 0,
        
        the rotational acceleration (α) of a rigid body about a fixed axis of rotation is caused by the net torque acting on the body:
        
        τ = I α
      - 2nd equilibrium condition :
        
        expresses rotational equilibrium:
        
        T = 0 (means that in equilibrium, there is no net external torque to cause rotation about any axis.)
        
        Conclusion :
        
        Conclusion :
        
        The first and second equilibrium conditions are stated in a particular reference frame. The first condition involves only forces and is therefore independent of the origin of the reference frame. However, the second condition involves torque, which is defined as a cross product.
- - - - The force required to accelerate the mass is supplied entirely by the lower thread, and the elastic limit of the lower thread is rapidly exceeded. The small movement of the mass before the lower thread breaks is easily accommodated by the elasticity of the upper thread without exceeding its elastic limit.
- - - - m1v1i + m2v2i = m1v1f + m2v2f
        
        Collision in one dimension
        
        Two objects collide, kinetic energy "CONSERVED"
        
        Collision in two or three dimensions
      - m1v1 + m2v2 = (m1+m2)vf
        
        Inelastic collision
        
        Some of kinetic energy is lost because it had been transferred
        
        Completely inelastic collision happen when the objects stick together afterward, so there is only one final velocity