ME 2320 Lecture Notes - Lecture 15: Angular Velocity, Relative Velocity
23 May 2018
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15.1
● Rigid body in translation:
○ At any given instant, all the points
of a rigid body in translaltion will have the same velocity and the same acceleration.
● Rigid body in rotation:
○The velocity of point P of a body rotating about a fixed axis is: , where r is the position vector drawn from anyv= ω × r
point
on the axis of rotation to point P.
○The acceleration of point P of a body rotating about a fixed axis is: ω )a= α × r+ ω × ( × r
● Equations relating the rotation of the slab and the motion of the points of the slab
○ , , ωv=rαat=rωan =r2
○ Need to remember that the velocity v and the component of the acceleration of a point P of the slab are tangent to the circular path described
at
by P. The normal component of the acceleration P is always directed toward the axis of rotation.
an
15.2
● General plane motion: can consider general plane motion to be the sum of translational and rotational motion
.
● Whenever possible, determine the velocity of the points of the body where it is connected to another body whose motion is known.
That other body may be an arm or crank rotating with a given angular velocity.
●Drawing diagram
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● Relative velocity formula: , or for plane motion: vB=vA+vB/AkvB=vA+ ω × rB/A
15.3
● Instantaneous center of rotation: serves as alternative way of solving problems involving the velocities
(ICR can’t be used t
determine accelerations!) of the various points of a body in the plane motion. As its name suggests, is the point about which we can
assume the body is rotating at a given instant.
● Finding the instantaneous center of rotation:
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●
● Once you have determined the ICR, can determine the velocity of any point P of the body: 1. Draw a sketch of the body showingvP
point P, the ICR C, and . 2. Draw a line from P to the ICR C and measure or calculate the distance from P to C. 3. The velocity isωvP
a vector perpendicular to the line PC, of the same sense as , and with a magnitude of .ωP C)ωvP= (
15.4
Document Summary
At any given instant, all the points of a rigid body in translaltion will have the same velocity and the same acceleration. The velocity of point p of a body rotating about a fixed axis is: point on the axis of rotation to point p . The acceleration of point p of a body rotating about a fixed axis is: . Equations relating the rotation of the slab and the motion of the points of the slab an = r 2 at = r v = r v = r. , where r is the position vector drawn from any a = r + ( r. General plane motion: can consider general plane motion to be the sum of translational and rotational motion . Whenever possible, determine the velocity of the points of the body where it is connected to another body whose motion is known.
