Momentum/Collisions

Momentum  "An object in motion tends to continue in constant motion unless acted upon by an outside force."  This tendency, outlined in Newton's first law, is known as momentum. How strong this tendency is depends upon the amount of inertia the object has and its velocity.

Momentum  The more inertia (mass) an object has, or the greater its velocity, the stronger its tendency to continue moving in constant motion, and so the greater its momentum.  momentum=mass x velocity  p=mv  The units on this would be kgm/s or a Ns.—see p. 245

Conservation of Momentum  Conservation of momentum: Within a system the total amount of momentum remains constant.  p i = p f  m i v i = m f v f

Conservation of Momentum  In a collision between objects the total sum of momentum of all objects before the collision is equal to the total sum of momentum of all objects after the collision.  p ai + p bi = p af + p bf

Collisions  During a collision, momentum is transferred from one object to another. There are two main categories of collisions:  Elastic  Inelastic

Elastic Collisions  Elastic: in which the shape of the objects is maintained. In an elastic collision the objects remain separated after the collision.  Kinetic energy is conserved in an elastic collision, but not in an inelastic collision.

Inelastic Collisions  Inelastic: in which the shape of the objects is changed or deformed (Car crash, two balls of clay hitting one another) or in which they stick together (two train cars coupling, bug hitting a windshield.)  In a perfectly inelastic collision The objects only have one final mass and one final velocity because they are now connected.

Impulse  In order to change an object's momentum an outside force must act on it for a certain amount of time. This change in momentum is known as an impulse.  The units on this would be Ns. FΔt= Δ p=mv f -mv i  (known as Impulse-Momentum Theorum)

Impulse  A specific change in momentum may take place over a long period of time thereby creating a small force, or can take place in a short period of time creating a large force.  —see p. 251, 252

Angular Momentum  The rotational version of linear momentum is called angular momentum, and is determined by the mass, shape, and angular velocity of the object.  It is a separate quantity than linear momentum

Angular Momentum  Angular momentum is represented by “L”, and can be calcuated by:  L = I ω Remember, I represents Moment of Inertia, and ω represents angular velocity

Angular Momentum  Angular momentum is conserved for any closed system, which means that if the moment of inertia is increased, the angular velocity will decrease, and vice versa (see p. 254)

Angular Momentum  Another implication regards the direction of angular momentum of a spinning object.  The actual direction is not in the same direction as the linear motion, but along the axis of rotation.

Angular Momentum  According to L = Iω, if the angular velocity or the moment of inertia is high, than the angular momentum is high  Object will therefore resist any change in direction (see p. 256)