Find the acceleration in circular motion

In summary: Does the x component determine the y component in circular motion?Yes, the x component determines the y component.
  • #1
theerenwithther
3
0
Homework Statement
The object (ignore the size) is placed at (0, 1) when t = 0 and moves
along unit circle, centered at (0,0), in xy plane (0 < t < 1/√3
). The x component of velocity is +√3 which is constant. Evaluate the following quantities when t = 1 /2√3. (a) Direction of Acceleration (ex. x direction) (b) Tangential Acceleration (c) Radial Acceleration (d)
Magnitude of Acceleration
Relevant Equations
N/A
Hello ,
First of all , I am still new to circular motion or any motions in general and still relatively learning so please bear with me.

1 . The direction of the tangential acceleration is parallel to the net velocity and that of radial of perpendicular to the velocity. So the direction of net acceleration would be inwards the circle (?) but it seems too vague. There may be other ways to phrase or even calculate it.

2/3/4 . In the next part , my approach was to find velocity from its x component by using v(x) = vsin(theta) and differentiating that v to eventually get the tangential acceleration and calculate the remaining two from it. But the concept seems thin in logical vision and in actual calculation , there is a derivative of sin(theta) respect to t in all values , which makes my final answers very unlikely. Any help would be greatly appreciated. I would be even more delighted if you take time to thoroughly explain the whole process.

Thank you in advance,
 

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  • #2
theerenwithther said:
The direction of the tangential acceleration is parallel to the net velocity and that of radial of perpendicular to the velocity. So the direction of net acceleration would be inwards the circle (?) but it seems too vague. There may be other ways to phrase or even calculate it.
Yes, calculate it. What will you need to find first?
theerenwithther said:
there is a derivative of sin(theta) respect to t
So you will need to find what theta is as a function of t.
 
  • #3
hello ! thank you for the reply ! but how can I find the theta as function of t with the limited values that I am given ??
 
  • #4
theerenwithther said:
hello ! thank you for the reply ! but how can I find the theta as function of t with the limited values that I am given ??
Where will it be after time t?
 
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  • #5
haruspex said:
Where will it be after time t?
do I even have enough information to find it ??
 
  • #6
theerenwithther said:
do I even have enough information to find it ??
”The x component of velocity is +√3 which is constant.”
 
  • #7
theerenwithther said:
do I even have enough information to find it ??
Does the x component determine the y component in circular motion?
 

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This path can be either a perfect circle or an ellipse.

2. How is acceleration defined in circular motion?

In circular motion, acceleration is defined as the rate of change of an object's velocity as it moves along the circular path. This means that the direction of the object's velocity is constantly changing, resulting in a change in acceleration.

3. How is acceleration calculated in circular motion?

The formula for calculating acceleration in circular motion is a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius of the circular path. This formula is also known as centripetal acceleration.

4. What is the direction of acceleration in circular motion?

The direction of acceleration in circular motion is always towards the center of the circular path. This is because the object is constantly changing its direction, resulting in a change in acceleration towards the center.

5. How does the mass of an object affect its acceleration in circular motion?

The mass of an object does not affect its acceleration in circular motion. This is because acceleration in circular motion is dependent on the object's velocity and the radius of the circular path, not its mass.

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