Detailed Explanations
1. Basic Impulse Formula
Formula: J = F × Δt
Explanation: Impulse is the product of force applied on an object and the time duration for which it acts. When a constant force acts on a body, the impulse delivered equals the force multiplied by the time interval.
Example: A cricket ball receives a force of 200 N for 0.05 seconds. Impulse = 200 × 0.05 = 10 N·s
2. Impulse-Momentum Theorem
Formula: J = Δp = m(v – u)
Explanation: This fundamental theorem states that impulse equals the change in momentum. This is one of the most important relationships in physics, connecting force, time, and motion.
Example: A 2 kg ball changes velocity from 5 m/s to 15 m/s. Impulse = 2(15 – 5) = 20 kg·m/s
3. Dimensional Formula of Impulse
Formula: [M¹L¹T⁻¹]
Explanation: Since impulse = Force × Time, and Force has dimensions [MLT⁻²], multiplying by [T] gives [M¹L¹T⁻¹]. This is identical to the dimensional formula of momentum, confirming the impulse-momentum theorem.
4. Angular Impulse Formula
Formula: L = τ × Δt
Explanation: Angular impulse is the rotational equivalent of linear impulse. It represents the change in angular momentum when a torque acts over a time interval. This is crucial for understanding rotational collisions and spinning objects.
Example: A torque of 50 N·m acts on a wheel for 0.2 seconds. Angular impulse = 50 × 0.2 = 10 N·m·s
5. Angular Impulse Dimensional Formula
Formula: [M¹L²T⁻¹]
Explanation: Since angular impulse = Torque × Time, and Torque has dimensions [ML²T⁻²], multiplying by [T] gives [M¹L²T⁻¹]. This matches the dimensional formula of angular momentum.
Main Concepts for Students
Why Impulse Matters:
- Explains why airbags save lives (increase Δt, decrease F)
- Helps understand sports techniques (follow-through increases Δt)
- Essential for collision analysis in engineering
- Foundation for rocket propulsion calculations
Important Points:
- Impulse and momentum change are equivalent concepts
- Impulse is a vector quantity (has direction)
- Unit: 1 N·s = 1 kg·m/s
- Greater impulse can result from either larger force or longer time
- In elastic collisions, impulse changes direction but kinetic energy is conserved
Impulse Formula FAQs
Q. What is the formula for impulse in physics?
The basic impulse formula is J = F × Δt (force multiplied by time interval). The impulse-momentum theorem states J = Δp = m(v – u), showing that impulse equals the change in momentum of an object.
Q. What is impulse formula in Class 11?
In Class 11 physics, impulse is taught as J = F × Δt = m(v – u). Students learn that impulse is a vector quantity measured in N·s or kg·m/s, and it represents both the effect of force over time and the resulting change in momentum.
Q. What is the dimensional formula of impulse?
The dimensional formula of impulse is [M¹L¹T⁻¹]. This is derived from Force [MLT⁻²] × Time [T] = [MLT⁻¹], which is the same as the dimensional formula for momentum, confirming their equivalence.
Q. How do you calculate impulse from a force-time graph?
Impulse equals the area under the force-time graph. For constant force, it’s a rectangle (F × Δt). For variable force, use integration: J = ∫F dt. This graphical method is powerful for analyzing real-world scenarios.
Q. What is the difference between impulse and momentum?
Momentum (p = mv) is a property of a moving object. Impulse (J = FΔt) is what causes momentum to change. The relationship is: Impulse = Change in momentum. Momentum is a state; impulse is an action.
Q. What is the angular impulse formula?
Angular impulse is given by L = τ × Δt, where τ is torque and Δt is time. It can also be expressed as L = ΔL = I(ω₂ – ω₁), representing the change in angular momentum of a rotating object.
Q. What is the unit of impulse?
Impulse has two equivalent SI units: Newton-second (N·s) from F × Δt, and kilogram-meter per second (kg·m/s) from momentum change. Both represent the same physical quantity: 1 N·s = 1 kg·m/s.
Q. How is impulse used in real-life applications?
Impulse principles explain: airbags (↑Δt, ↓F), cushioned shoes (↑Δt, ↓impact force), cricket bat follow-through (↑Δt, ↑ball velocity), crash barriers (↑Δt, ↓injury), and rocket thrust (continuous impulse creates momentum change).
Q. Can impulse be negative?
Yes, impulse can be negative because it’s a vector quantity. A negative impulse indicates force applied opposite to the chosen positive direction, resulting in a decrease in momentum in that direction. The sign indicates direction, not magnitude.
Q. What is the relationship between impulse and kinetic energy?
While impulse equals change in momentum (J = Δp), it doesn’t directly equal change in kinetic energy. However, for one-dimensional motion: if impulse J is known, ΔKE = J²/(2m) + J·u, where u is initial velocity. Energy is scalar; impulse is vector.
Practice Problem with Solution
Problem: A 0.5 kg ball moving at 10 m/s is struck by a bat and moves in the opposite direction at 15 m/s. The contact time is 0.02 seconds. Calculate: (a) impulse, (b) average force.
Solution:
- Taking initial direction as positive: u = +10 m/s, v = -15 m/s
- (a) J = m(v – u) = 0.5(-15 – 10) = 0.5(-25) = -12.5 N·s
- (b) Favg = J/Δt = -12.5/0.02 = -625 N
The negative sign indicates force was applied opposite to the initial motion direction.
Note for Students: Understanding impulse is crucial for mechanics, collision theory, and real-world applications. Master these formulas by practicing numerical problems and connecting concepts to everyday phenomena like sports, vehicle safety, and engineering design.
