momentum

Examples of momentum in the following topics:

• Rotational Collisions

  • In a closed system, angular momentum is conserved in a similar fashion as linear momentum.
  • Is momentum still conserved ?
  • Angular momentum is defined, mathematically, as L=Iω, or L=rxp.
  • Units for linear momentum are kg⋅m/s while units for angular momentum are kg⋅m2/s.
  • So rotating objects that collide in a closed system conserve not only linear momentum p in all directions, but also angular momentum L in all directions.

• Linear Momentum

  • In classical mechanics, linear momentum, or simply momentum (SI unit kg m/s, or equivalently N s), is the product of the mass and velocity of an object.
  • Momentum is conserved in both inelastic and elastic collisions.
  • Keep in mind that momentum and velocity are vectors.
  • Momentum, like energy, is important because it is conserved.
  • Total momentum of the system (or Cradle) is conserved.

• Conservation of Angular Momentum

  • The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
  • The symbol for angular momentum is the letter L.
  • Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero.
  • If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,
  • Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum.

• Impulse

  • However, changing momentum is also related to how long a time the force acts.
  • $F = \frac {\Delta p}{\Delta t}$ (Δp: change in momentum) ,
  • Impulse is always equal to change in momentum and is measured in Ns (Newton seconds), as both force and the time interval are important in changing momentum.
  • The area under the curve has units of momentum and is equal to the impulse or change in momentum between times t1 and t2.
  • A brief overview of momentum and impulse for high school physics students.

• Relativistic Momentum

  • Conservation laws in physics, such as the law of conservation of momentum, must be invariant.
  • It is important to note that for speeds much less than the speed of light, Newtonian momentum and relativistic momentum are approximately the same.
  • As one approaches the speed of light, however, relativistic momentum becomes infinite while Newtonian momentum continues to increases linearly.
  • This figure illustrates that relativistic momentum approaches infinity as the speed of light is approached.
  • Newtonian momentum increases linearly with speed.

• Momentum, Force, and Newton's Second Law

  • Therefore, total momentum (p1+p2) is constant.
  • Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero, so the total change in momentum is zero.
  • Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes.
  • First, note that the change in momentum Δp is given by Δp=Δ(mv).
  • Therefore, the total momentum of the balls is conserved.

• Energy and Momentum

  • Electromagnetic waves have energy and momentum that are both associated with their wavelength and frequency.
  • These photons are strictly defined as massless, but have both energy and surprisingly, given their lack of mass, momentum, which can be calculated from their wave properties.
  • And, given that he related energy and mass (E=mc2), it becomes more conceivable that a wave (which has an energy value) not only has an equation to mass but a momentum as well.
  • And indeed, Einstein proved that the momentum (p) of a photon is the ratio of its energy to the speed of light.
  • Substituting E with hc/λ cancels the c terms, making momentum also equal to the simple ratio of Planck's constant to wavelength.

• Internal vs. External Forces

  • Net external forces (that are nonzero) change the total momentum of the system, while internal forces do not.
  • Forces external to the system may change the total momentum when their sum is not 0, but internal forces, regardless of the nature of the forces, will not contribute to the change in the total momentum.
  • Whether the total kinetic energy of the pucks is conserved or not, total momentum is conserved.
  • Total momentum of the system (or Cradle) is conserved.
  • Contrast the effects of external and internal forces on linear momentum and collisions

• Accretion Disks

  • The preceding section ignores an important aspect of accretion: the angular momentum of the accreta.
  • If the material starts with some net angular momentum it can only collapse so far before its angular velocity will be sufficient to halt further collapse.
  • First let's see why angular momentum can play a crucial role in accretion.
  • The initial specific angular momentum is $v b$.
  • If the material conserves angular momentum we can compare the centripetal acceleration with gravitational acceleration to give

• Gyroscopes

  • A gyroscope is a device for measuring or maintaining orientation based on the principles of angular momentum.
  • With the wheel rotating as shown, its angular momentum is to the woman's left.
  • The torque produced is perpendicular to the angular momentum, thus the direction of the angular momentum is changed, but not its magnitude.
  • This torque causes a change in angular momentum ΔL in exactly the same direction.
  • Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces.