Displacement of an object in circular motion

In summary, the object undergoing circular motion has an angular frequency of 1 rad/s. The displacement of the object in the x-direction can be represented by the equation x=Acos(ωT+δ), where ω is the angular frequency and δ is the phase angle. The displacement of the object in the y-direction can be represented by the equation y=Asin(ωT+δ). At t=0s, the y-displacement of the object is 0. The first time after t=0s that y=0 is when the object completes half a period, which is equal to 1/2T or π/ω.
  • #1
jami8337
26
0

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
 
Physics news on Phys.org
  • #2
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)?
 

What is the displacement of an object in circular motion?

The displacement of an object in circular motion is the shortest distance and direction between the starting point and ending point of the object's motion. It is a vector quantity, meaning it has both magnitude and direction.

How is displacement different from distance in circular motion?

Distance is the total length of the path traveled by the object, while displacement is the straight-line distance between the starting and ending points. In circular motion, the distance and displacement are the same only if the object completes one full revolution.

Can an object's displacement be zero in circular motion?

Yes, an object's displacement can be zero in circular motion if it starts and ends at the same point. This can happen if the object completes a full revolution or if it moves in a circular path with a constant radius.

How is displacement calculated in circular motion?

Displacement in circular motion can be calculated using the formula Δx = rΘ, where Δx is the displacement, r is the radius of the circle, and Θ is the angle of rotation. This formula is based on the relationship between the circumference of a circle and its radius.

Is the displacement of an object in circular motion always constant?

No, the displacement of an object in circular motion is not always constant. It depends on the speed and direction of the object's motion. If the object is moving at a constant speed, the displacement will remain constant. However, if the speed or direction changes, the displacement will also change accordingly.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
577
  • Introductory Physics Homework Help
Replies
6
Views
719
  • Introductory Physics Homework Help
Replies
8
Views
695
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
2
Replies
38
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
156
  • Introductory Physics Homework Help
Replies
16
Views
387
  • Introductory Physics Homework Help
Replies
6
Views
947
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top