Kinematic questions(velocity of 2 contact points)

In summary, the conversation discusses how to determine the velocity of the contact point of the right rod at any given time, based on the angular velocity of the left rod and the distance from the contact point to the centre of the left gear. The relationship between the two velocities changes when the two rods are parallel, and it is important to consider the geometry of the rods in determining the velocity. The equation ωrLr = ωlrl + v is used, where v represents the tangential velocity component of the end of the right rod in the direction of the radius vector rl. The exact value of v should be determined based on the angle between the two rods at the current time.
  • #1
hihiip201
170
0
in the picture below



http://tinypic.com/view.php?pic=9riq9l&s=6


if we know the angular velocity of the gear on the left, as well as their current distance from contact point, what can we say about the velocity of the right rod at the contact point at anytime t?


we know it is not just the velocity of the contact point of the left rod because the right rod can be sliding along the left rod. but how do we find its exact velocity?
 
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  • #2
hihiip201 said:
in the picture below
http://tinypic.com/view.php?pic=9riq9l&s=6if we know the angular velocity of the gear on the left, as well as their current distance from contact point, what can we say about the velocity of the right rod at the contact point at anytime t?we know it is not just the velocity of the contact point of the left rod because the right rod can be sliding along the left rod. but how do we find its exact velocity?
If you know the angular velocity of the left rod and the distance of the contact point from the centre of the left gear (rl), you can determine the velocity of the contact point (ie. in terms of ωl and rl). You then just have to relate that to the velocity of the contact point on the right rod. That relationship changes at the point where the two rods are parallel (contact point is the whole rod). So you would have to break it down into two parts (ie. one where the end of the right rod contacts the left and the other where the end of the left rod contacts the right).

AM
 
  • #3
Andrew Mason said:
If you know the angular velocity of the left rod and the distance of the contact point from the centre of the left gear (rl), you can determine the velocity of the contact point (ie. in terms of ωl and rl). You then just have to relate that to the velocity of the contact point on the right rod. That relationship changes at the point where the two rods are parallel (contact point is the whole rod). So you would have to break it down into two parts (ie. one where the end of the right rod contacts the left and the other where the end of the left rod contacts the right).

AM


how exactly do we relate the velocity of the contact point of left rod and right rod?

we know the velocity of left rod at contact point, but certainly right rod's velocity at the contact point wouldn't be the same since it is sliding along the left rod right?
 
  • #4
hihiip201 said:
how exactly do we relate the velocity of the contact point of left rod and right rod?

we know the velocity of left rod at contact point, but certainly right rod's velocity at the contact point wouldn't be the same since it is sliding along the left rod right?
You have to work it out from the geometry.

Consider the situation shown with the tip of the right rod is contacting the body of the left rod. You have to relate the velocity of the tip of the right rod to the velocity of the point that it is in contact with:

ωrLr = ωlrl + v where v is the speed of the end of the right rod along the length of the left rod (ie. drl/dt)/

I haven't worked it out but I think that is how you have to do it. The trick is to express v in terms of the angular velocities of the two rods.

AM
 
  • #5
Andrew Mason said:
You have to work it out from the geometry.

Consider the situation shown with the tip of the right rod is contacting the body of the left rod. You have to relate the velocity of the tip of the right rod to the velocity of the point that it is in contact with:

ωrLr = ωlrl + v where v is the speed of the end of the right rod along the length of the left rod (ie. drl/dt)/

I haven't worked it out but I think that is how you have to do it. The trick is to express v in terms of the angular velocities of the two rods.

AM



my first guess is also the equation you have above, but what i have trouble is that, should vector v in your equation be based on the geometry of the two rods at current time t? or t = t +dt? to be it makes more sense to use the time at t+dt or else the left rod will end up in a awkward position.
 
  • #6
hihiip201 said:
my first guess is also the equation you have above, but what i have trouble is that, should vector v in your equation be based on the geometry of the two rods at current time t? or t = t +dt? to be it makes more sense to use the time at t+dt or else the left rod will end up in a awkward position.
v is just the component of the tangential velocity of the end of the right rod that is in the direction of the radius vector rl. So it is based on the angle between the two rods.

AM
 
  • #7
Andrew Mason said:
v is just the component of the tangential velocity of the end of the right rod that is in the direction of the radius vector rl. So it is based on the angle between the two rods.

AM


right but the angle between two rods at the current time? or some dt later??


if I break the velocity into two component, the component that is along the contact point of left rod , and the velocity tangential to the left rod.

After some dt later, the position of the contact point of my right rod would be a the position of the contact point of the left rod, minus some distance away from the center of the left rod.


I don't know if my question make sense, sorry about the confusion.
 
  • #8
hihiip201 said:
right but the angle between two rods at the current time? or some dt later??
It does not matter. dt is arbitrarily small. If you set v(t) at t then at t+dt it will be v(t+dt) = v + dv. If you set θ(t) at t then at t+dt it will be θ(t+dt) = θ+dθ = θ+ω(dt)

if I break the velocity into two component, the component that is along the contact point of left rod , and the velocity tangential to the left rod.

After some dt later, the position of the contact point of my right rod would be a the position of the contact point of the left rod, minus some distance away from the center of the left rod.
What you want to find is the velocity of the contact point on the left rod. Can you express that in terms of the velocity of the end of the right rod? ie. break down the tangential velocity of the right rod ωrrr into components that are in the direction of the rl and perpendicular to that direction (ie tangential to rl).

AM
 

What are kinematic questions?

Kinematic questions are questions that involve the study of motion and its causes without considering the forces that cause the motion.

What is the velocity of 2 contact points?

The velocity of 2 contact points refers to the speed and direction of movement at two points that are in contact with each other. It can be calculated using the distance between the two points and the time it takes for one point to reach the other.

How is velocity measured?

Velocity is measured as the rate of change of an object's position with respect to time. It is typically measured in units of distance per time, such as meters per second or kilometers per hour.

What factors can affect the velocity of 2 contact points?

The velocity of 2 contact points can be affected by factors such as the distance between the points, the speed of the objects at each point, the direction of movement, and any external forces acting on the objects.

Why is the study of kinematics important?

The study of kinematics is important because it allows us to understand and predict the motion of objects without having to consider the complex forces acting on them. This knowledge is essential in many fields, including engineering, physics, and sports science.

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