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t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect. [3] The linear momentum of a rigid body is the product of the mass of the body and the velocity of its center of mass v cm. [1] [4] [5]
The momentum of the object at time t is therefore p(t) = m(t)v(t). One might then try to invoke Newton's second law of motion by saying that the external force F on the object is related to its momentum p(t) by F = dp / dt , but this is incorrect, as is the related expression found by applying the product rule to d(mv) / dt : [17]
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. [1] [2]
The area rule is a corollary of the angular momentum law in the form: The resulting moment is equal to the product of twice the mass and the time derivative of the areal velocity. [ 10 ] It refers to the ray r → {\displaystyle {\vec {r}}} to a point mass with mass m .
At time t, let a mass m travel at a velocity v, meaning the initial momentum of the system is p 1 = m v {\displaystyle \mathbf {p} _{\mathrm {1} }=m\mathbf {v} } Assuming u to be the velocity of the ablated mass d m with respect to the ground, at a time t + d t the momentum of the system becomes
Momentum (N⋅s) Explanation 0.42 2.4 1 A 420-gram (15 oz) football (FIFA specified weight for outdoor size 5) kicked to a speed of 8.6 km/h (5.3 mph). 0.42 38 16 The momentum of the famous football kick of the Brazilian player Roberto Carlos in the match against France in 1997. The football had a speed of 137 km/h (85 mph), making it one of ...