- A piece of dust finds itself on a CD. The spin rate of the CD is omega rpm, and the piece of dust is r cm from the center. The CD rotates for 2.5 minutes. (Ignore the forces and acceleration needed to set and keep the CD in motion; only consider the piece of dust)
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![c) Choose the equation of motion to calculate the total angular displacement traveled by the dust in
2.5 minutes from the list below:
1
1.40=0-00= wt
2. w = wo+at
3.40 =0-0₁ = w₁t+at²
4. w² = w²+2a40
d) Calculate the total angular displacement and the distance s traveled by the dust particle in 2.5
mins.
ΔΘ = 15.7
S=
rad
m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e392a71-e7bd-4981-938b-8b094393c2fe%2F75480c06-bb70-4682-989d-960a5416bdb0%2Fxnibax_processed.jpeg&w=3840&q=75)
![1. A piece of dust finds itself on a CD. The spin rate of the CD is omega rpm, and the piece of dust is r
cm from the center. The CD rotates for 2.5 minutes. (Ignore the forces and acceleration needed to set
and keep the CD in motion; only consider the piece of dust)
a) Which quantities are constant during the spinning of the dust particle along with the CD?
Both Angular Velocity ar
b) SET UP
Using the notation A0 for angular displacement, 0 for angular position at time t, 0 for the
initial angular position, w for angular velocity at time t, wo for the initial angular velocity,
and a for the angular acceleration, and r for the distance of the particle from the center,
determine what quantities are known and what are unknown.
●
. Enter some known values below.
t = 2.5
min
r=r
a=
W =
cm
rad/s²
rpm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e392a71-e7bd-4981-938b-8b094393c2fe%2F75480c06-bb70-4682-989d-960a5416bdb0%2Frzhhlo_processed.jpeg&w=3840&q=75)
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