In the formula L = Iω, what does I represent?
Inertia
Moment of inertia
Impulse
Intensity
Angular momentum is a fundamental concept in physics that describes the rotational motion of objects. When it comes to understanding how objects behave when they rotate, the angular momentum formula is crucial. This formula provides a quantitative measure of the amount of rotation an object has, considering its mass, shape, and speed.
The angular momentum formula is expressed as
There is another way to express angular momentum for point particles, which is
The concept of angular momentum was first introduced by Sir Isaac Newton in his seminal work Principia Mathematica. He described it as the “quantity of motion” of rotating bodies, which today we define more precisely with the formulas above. Newton’s development of the laws of motion and universal gravitation laid the groundwork for later physicists to explore and formalize the principles of angular momentum in various physical contexts.
Question: A wheel with a moment of inertia of 0.75 kg·m² spins at a rate of 150 revolutions per minute (rpm). Calculate its angular momentum.
Solution:
First, convert rpm to radians per second: 𝜔 =150 × (2𝜋 / 60) =15.7 rad/s
Use the angular momentum formula 𝐿=𝐼 x 𝜔:
𝐿 = 0.75 × 15.7 = 11.775 kg\cdotpm²/s
Answer: The angular momentum of the wheel is 11.775 kg·m²/s.
Question: A particle of mass 2 kg is moving at a velocity of 4 m/s in a straight line. It passes through a point which is 0.5 m perpendicular distance from the origin. Find the angular momentum of the particle about the origin.
Solution:
The linear momentum p of the particle is given by 𝑝 = 𝑚𝑣 = 2 × 4 = 8 kg\cdotpm/s.
Using 𝐿 = 𝑟 × 𝑝, and since the perpendicular distance r and p are at right angles, 𝐿 = 𝑟 x 𝑝:
𝐿 = 0.5 × 8 = 4 kg\cdotpm²/s
Answer: The angular momentum of the particle about the origin is 4 kg·m²/s.
Question: A solid disk with a radius of 0.2 m has a mass of 3 kg. If it rotates at 200 rpm, calculate its angular momentum. Assume the disk is a solid cylinder with 𝐼=(1 / 2) 𝑀𝑅².
Solution:
Convert rpm to radians per second:
𝜔 = 200 × (2𝜋 / 60) = 20.94 rad/s
Calculate the moment of inertia for the disk:
𝐼 = (1 / 2) × 3 × (0.2)² = 0.06 kg\cdotpm²
Calculate angular momentum using 𝐿=𝐼𝜔:
𝐿 = 0.06 × 20.94 = 1.2564 kg\cdotpm²/s
Answer: The angular momentum of the disk is approximately 1.2564 kg·m²/s.
The formula for angular momentum about any point is L = r × p, where r is the position vector and p is the linear momentum.
Calculate angular momentum using L = Iω for rigid bodies, where I is the moment of inertia and ω is the angular velocity.
Yes, angular momentum changes with radius; it is directly proportional to the radius (r) in the formula L = r × p.
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In the formula L = Iω, what does I represent?
Inertia
Moment of inertia
Impulse
Intensity
What is the formula for angular momentum of a particle?
L = Iω
L = r × p
L = mvr
All of the above
What is the unit of angular momentum?
kg·m²/s
kg·m/s²
kg·m/s
N·m
What happens to the angular momentum if the moment of inertia of a rotating body is doubled while the angular velocity remains constant?
It is halved
It remains the same
It is doubled
It is quadrupled
Which of the following represents the conservation of angular momentum?
ΔL = 0
Δp = 0
ΔE = 0
ΔF = 0
If a figure skater pulls in her arms during a spin, what happens to her angular velocity?
It decreases
It increases
It remains the same
It becomes zero
In the context of angular momentum, what does ω represent?
Angular displacement
Angular velocity
Linear velocity
Rotational inertia
A particle has a linear momentum p and is at a distance r from the axis of rotation. What is the formula for its angular momentum?
L = p × r
L = r × p
L = mvr
L = Iω
If the mass of a rotating object is tripled, what happens to its angular momentum, assuming radius and velocity remain constant?
It remains the same
It is tripled
It is doubled
It is halved
Which physical principle states that in the absence of an external torque, the total angular momentum of a system remains constant?
Conservation of energy
Conservation of linear momentum
Conservation of angular momentum
Conservation of mass
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