Displacement of an object in circular motion

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SUMMARY

The discussion focuses on the analysis of an object in circular motion, specifically addressing angular frequency and displacement equations. The angular frequency (ω) was calculated as 1 rad/s using the formula ω = 2π/T, where T is the period derived from T = 2πr/v. The user seeks guidance on formulating the displacement equations for both the x and y directions, utilizing the equation x = A cos(ωT + δ) and is prompted to define values for ω and δ to proceed with the y-displacement equation.

PREREQUISITES
  • Understanding of circular motion principles
  • Familiarity with angular frequency calculations
  • Knowledge of trigonometric functions in physics
  • Ability to apply kinematic equations
NEXT STEPS
  • Learn how to derive the equation for y-displacement in circular motion
  • Study the relationship between angular frequency and linear velocity
  • Explore the concept of phase angle (δ) in harmonic motion
  • Investigate the implications of initial conditions on displacement equations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to clarify concepts related to angular frequency and displacement equations.

jami8337
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Homework Statement


A1. An object undergoing circular motion is pictured below at time t = 0 s.
(a) What is the angular frequency of the object?
(b) What is the equation of the displacement of the object in the x-direction?
(c) What is the equation of the displacement of the object in the y-direction?
(d) What is the y-displacement of the object at t = 0 s?
(e) What is the first time after t = 0 s that y = 0?

I can't put the diagram on here but its a circle on x/y axis with the object in the lower right quadrant where θ=45° and v=2m/s and the r=2m

Homework Equations


T=2∏r/v
ω=2∏/T
x=Acos(ωT+δ)

The Attempt at a Solution


Ive managed to do part (a) using the equations above and got 1rad/s
However I am not sure on the rest, i was thinking of using x=Acos(ωT+δ) but I am not sure how

cheers for any advice
 
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jami8337 said:

Homework Statement


A1. An object undergoing circular motion is pictured below at time t = 0 s.
(a) What is the angular frequency of the object?
(b) What is the equation of the displacement of the object in the x-direction?
(c) What is the equation of the displacement of the object in the y-direction?
(d) What is the y-displacement of the object at t = 0 s?
(e) What is the first time after t = 0 s that y = 0?

I can't put the diagram on here but its a circle on x/y axis with the object in the lower right quadrant where θ=45° and v=2m/s and the r=2m

Homework Equations


T=2∏r/v
ω=2∏/T
x=Acos(ωT+δ)

The Attempt at a Solution


Ive managed to do part (a) using the equations above and got 1rad/s
However I am not sure on the rest, i was thinking of using x=Acos(ωT+δ) but I am not sure how
Yes, carry on with that. What values do you ascribe to ω and δ? What equation will you write for y(t)?
 

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