How Can You Determine the Kinematics of Rigid Body BD in a Rotating System?

In summary, the question is asking to determine the angular velocity and angular acceleration of rod BD, as well as the velocity and acceleration of collar D, for values of theta from 0 to 360 degrees. The given information is that crank AB has a constant angular velocity of 160rpm counterclockwise. The equation used is lambda=160rpm=160(2pi/60)rad/s. The solution requires finding the equation for beta (angle of bar BD from the horizontal) in order to plug in values for theta. The length of AB and BD, as well as the vertical component of AD, are also known. Using this information, the vertical component of BD can be found, which is BD.Sin(beta).
  • #1
chart2006
12
0

Homework Statement


"Knowing that crank AB has a constant angular velocity of 160rpm counterclockwise, determine and plot, for values of [tex]\theta [/tex] from 0 to 360 degrees, (a) the angular velocity and angular acceleration of rod BD, (b) the velocity and acceleration of collar D.
http://www.mypicx.com/uploadimg/557399749_04082009_1.jpg

Homework Equations



I don't know! :(


The Attempt at a Solution



[tex]\lamda =160rpm=160(\frac{2\pi}{60})rad/s[/tex]

Unfortunately this is as far as I've been able to get. The reason is because I'm not sure as how to derive an equation that would allow me to plug in a value from 0 to 360 for theta and it give me beta (angle of bar BD from the horizontal). If I can just get past that point I can figure the rest out. With any other problem there is a fixed position in which I can just use the triangle method to figure it out but i can't really do that here.
 
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  • #2
hi chart 2006

you know then length AB & BD and the also the vertical component of AD

the vertical component of AB is AB.Sin(theta) from this you should be able to find the vertical component of BD, ie BD.Sin(beta)...
 

1. What is the difference between kinematics and dynamics?

Kinematics is the study of motion without considering the forces that cause the motion, while dynamics is the study of motion including the forces and torques that cause it.

2. What is a rigid body?

A rigid body is a theoretical object that does not deform or change shape when subjected to external forces or torques. It is used in kinematic analysis to simplify the study of motion.

3. How is the motion of a rigid body described?

The motion of a rigid body is described using displacement, velocity, and acceleration. These are vector quantities that describe the position, speed, and change in speed of the body, respectively.

4. What is the difference between translational and rotational motion?

Translational motion refers to the movement of a rigid body in a straight line, while rotational motion refers to the movement of a rigid body around an axis. Both types of motion can occur simultaneously in a rigid body.

5. How is the motion of a rigid body affected by external forces?

The motion of a rigid body is affected by external forces according to Newton's laws of motion. These laws state that the motion of a body is determined by the net force acting on it, and the direction of its acceleration is in the same direction as the net force.

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