Angular Velocity: Find Angular Velocity of A w.r.t B using Radii & ω

We need to find the angular velocity of particle A with respect to particle B. This can be calculated using the formula ω₁₂ = (|V perpendicular|)/(vector R), where ω₁₂ is the angular velocity of A with respect to B, |V perpendicular| is the component of velocity perpendicular to the direction of vector R, and vector R is the distance between particles A and B. However, it is important to note that the linear velocity of both particles must be the same for this formula to be accurate.
  • #1
vickyiit
3
0

Homework Statement



radii R₁, R₂, angular velocity ω₁, ω₂

Homework Equations



Two particles 1 and 2 describe co-planar concentric circles of radii R₁ and R₂ with angular velocities ω₁ and ω₂ as shown in the figure. Find the angular velocity of A with respect to B.

The Attempt at a Solution



Θ will be constant as particles are moving with constant velocity. therefore, ω₁₂=(|V perpendicular|)/(vector R). But i am not sure whether i proceeded right. Please help.
 

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  • #2
You've got to a good start by correctly understanding that both particles are moving at constant "velocity". What you don't mention is... what velocity? The same linear or angular velocity?

;-)
 
  • #3
mezarashi said:
You've got to a good start by correctly understanding that both particles are moving at constant "velocity". What you don't mention is... what velocity? The same linear or angular velocity?

;-)

angular velocity
 

FAQ: Angular Velocity: Find Angular Velocity of A w.r.t B using Radii & ω

What is angular velocity?

Angular velocity is the measurement of the rate of change of angular displacement of an object with respect to time. It is a vector quantity that describes how fast an object is rotating around a specific point or axis.

How is angular velocity calculated?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. The formula for angular velocity is ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angular displacement, and Δt is the change in time.

What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are related by the radius of rotation. The linear velocity of an object is equal to the product of its angular velocity and the distance from the axis of rotation. This relationship is expressed as v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of rotation.

How can I find the angular velocity of an object using radii and ω?

To find the angular velocity of an object using radii and ω, you can use the formula ω = v/r, where v is the linear velocity and r is the radius of rotation. Alternatively, you can also use the formula ω = Δθ/Δt, where Δθ is the change in angular displacement and Δt is the change in time.

Why is it important to calculate angular velocity?

Calculating angular velocity is important in understanding the rotational motion of objects. It is also essential in many engineering and scientific applications, such as designing machines, analyzing the motion of celestial bodies, and understanding the dynamics of fluids and gases.

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