What is Momentum?
Momentum is a term that is highly used in sports. When it is said that a team has momentum, it is a bit difficult to defeat the team. Momentum is a term that is associated with Physics, and it means the amount of motion contained in a body. When an object is in motion, it is said to have some momentum.
In simple words, momentum is defined as "mass in motion". All the objects possess some mass, and when an object moves, it has momentum, i.e., it has its mass in motion. The momentum of an object depends upon two parameters, firstly the mass of the object and secondly the velocity at which the object is moving. So momentum depends upon the mass and the velocity of the object.
Derived Unit of Momentum
In mathematical terms, the momentum of an object is the product of the mass of the object and its velocity.
Momentum = mass * velocity
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In physics, the momentum of an object is denoted by 'p'. So the equation can be written as,
p = m * v
Where,
m = mass of the body, and
v = velocity of the body
The above equation describes that the momentum of a body is directly proportional to the mass & its velocity.
The si unit of momentum in physics is the product of units of mass and velocity. The unit of mass is kg, and that of velocity is
ms-1 s-1
Hence, the SI unit of momentum is kgm/s⁻¹.
Other Momentum Units
Let us consider a situation in which the applied force is equal to the rate of change of momentum of the object. So,
Force = rate of change of momentum
or
Force = (change in momentum)/(time interval) then,
Change in momentum = Force * (time interval).
Hence, the SI unit for momentum in physics can also be Newton-second (Ns).
In the CGS system, the mass of an object is considered in grams, and velocity is considered in terms of centimeters per second. Therefore, the unit of momentum is gram-centimeters per second (g⋅cm/s).
The standard unit of momentum is kg*m/s. There are some other units of momentum viz: kg*mi/hr, kg*km/hr, and g*cm/s. In each of these units, the unit of mass of the object is multiplied by the unit of the velocity of the object.
Impulse
In Classical Mechanics, Impulse ( represented by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector volume, the impulse is also a vector volume. Impulse applied to an object produces an original vector change in its direct instigation, also in the attendant direction. The SI unit of impulse is the Newton second (Ns), and the dimensionally original unit of instigation is the kilogram cadence per second (kg ⋅ m/ s). The corresponding English engineering unit is the pound-second (lbf ⋅ s), and in the British Gravitational System, the unit is the slug- bottom per second (slug ⋅ ft/ s).
An attendant force causes acceleration and a change in the haste of the body for as long as it acts. An attendant force applied over a longer time, thus, produces a bigger change in direct instigation than the same force applied compactly; the change in instigation is equal to the product of the average force and duration. Again, a small force applied for a long time produces the same change in instigation — the same impulse — as a larger force applied compactly.
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FAQs on Unit of Momentum
1. What are the common units used to measure momentum in Physics?
The standard unit of momentum depends on the system of measurement. In the SI (International System of Units), the unit of momentum is kilogram-meter per second (kg⋅m/s). This is derived from the product of the SI unit for mass (kg) and the SI unit for velocity (m/s). Another valid SI unit is the Newton-second (N·s). In the CGS (Centimetre-Gram-Second) system, the unit is gram-centimetre per second (g⋅cm/s).
2. How is momentum calculated, and what do the variables in its formula represent?
Momentum is calculated using the formula p = m × v. In this equation:
- p represents the momentum of the object.
- m stands for the mass of the object, which is a measure of the matter it contains.
- v represents the velocity of the object, which is its speed in a specific direction.
3. Why is momentum considered a vector quantity and not a scalar quantity?
Momentum is a vector quantity because it is the product of a scalar quantity (mass) and a vector quantity (velocity). Since velocity has both magnitude (speed) and direction, the resulting momentum also has both magnitude and direction. For example, to fully describe the momentum of a moving car, you must state not only how much momentum it has (e.g., 20,000 kg⋅m/s) but also the direction it is travelling (e.g., eastward).
4. How can momentum be expressed in terms of Newton-seconds (N·s)?
The unit Newton-second (N·s) for momentum comes from Newton's Second Law of Motion. The law states that the net force (F) applied to an object equals the rate of change of its momentum (Δp) over time (Δt), or F = Δp / Δt. By rearranging this formula, we find that the change in momentum (which is also momentum) is Δp = F × Δt. Since the SI unit for force is the Newton (N) and for time is the second (s), the unit for momentum can be expressed as Newton-second (N·s).
5. What are some real-world applications that demonstrate the importance of momentum?
The concept of momentum is crucial in many real-world scenarios. For example:
- In vehicle safety design, crumple zones in cars are designed to increase the time of impact during a collision, which reduces the force experienced by passengers by changing the car's momentum more gradually.
- In sports, a bowler in cricket or a pitcher in baseball runs before releasing the ball to impart greater momentum to it, making it travel faster.
- In rocket propulsion, a rocket moves forward by expelling gas backward at high velocity. The total momentum is conserved, so the forward momentum gained by the rocket equals the backward momentum of the expelled gas.
6. What is the difference between 'momentum' and 'moment of a force' (or torque) in physics?
Students often confuse momentum and moment of a force (torque), but they describe different physical concepts:
- Momentum (p) is related to an object's linear motion. It is defined as mass times velocity (p = mv) and describes the quantity of motion an object has. Its SI unit is kg⋅m/s.
- Moment of a Force (τ), or torque, is related to an object's rotational motion. It measures the effectiveness of a force in causing an object to rotate about an axis. It is defined as force times the perpendicular distance from the axis (τ = r × F). Its SI unit is the Newton-meter (N·m).
7. Can an object with a very large mass have zero momentum? Explain how.
Yes, an object with a very large mass can have zero momentum. Momentum is the product of mass and velocity (p = m × v). If an object's velocity is zero, it is not moving. In this case, no matter how large its mass is, its momentum will be zero because multiplying any mass by zero results in zero. For example, a massive truck or a large building has zero momentum when it is at rest.
8. What is the dimensional formula for momentum, and how is it derived?
The dimensional formula for momentum is [MLT⁻¹]. This is derived from its physical formula, p = mass × velocity. The dimensional symbol for mass is [M]. The dimensional formula for velocity (distance/time) is [LT⁻¹]. Therefore, by combining them, the dimensions of momentum become [M] × [LT⁻¹] = [MLT⁻¹]. This formula is essential for checking the consistency of physics equations involving momentum.
