Find angular velocity given velocity of attached block

This means that ωAB = 2.40 rad/s.In summary, at the instant shown, the angular velocity of bar AB is 2.40 rad/s. This is obtained by setting vB equal to vC, assuming ωAB = ωBC = 0, and using the fact that the length of rBC is constant and there is no component of v in the i direction.
  • #1
grekin
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Homework Statement



The block at C is moving downward at vc = 4.8 ft/s. Determine the angular velocity of bar AB at the instant shown.

Hibbler.ch16.p58_new.jpg


Homework Equations



x = cross product
r = distance to point from frame of reference
Boldface will indicate vectors
v = ω x r
vB = vA + ω x rB/A = vA + vB/A

The Attempt at a Solution



vB = ωAB x rB/A = -2*ω[itex]\vec{j}[/itex]
vC = vB + ω x rC/B
-4.8[itex]\vec{j}[/itex] = -2*ω[itex]\vec{j}[/itex]+(-ω[itex]\vec{k}[/itex] x (3cos(30)[itex]\vec{i}[/itex]+3sin(30)[itex]\vec{j}[/itex]))

Taking the cross product and setting the y-components equal to each other, I get ωAB=1.04 rad/s. The correct answer is ωAB = 2.40 rad/s. From working backwards, I believe the correct answer can be obtained by setting vB equal to vC:

-4.8[itex]\vec{j}[/itex] = -2*ω[itex]\vec{j}[/itex]

If this is correct, my question is why can they be set equal to each other while disregarding ωBC and rC/B?
 
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  • #2
In your attempt at a solution you assumed that ωAB = ωBC which is not the case.

The length of rBC is constant and at the instant in time there is no component of v in the i direction. Therefore, ωBC = 0 and vB = vC.
 
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1. What is angular velocity?

Angular velocity is a measure of the rate of change of angular displacement of an object. It is the rotational equivalent of linear velocity and is measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related by the radius of the circle through which the object is moving. The formula for this relationship is ω = v/r, where ω is angular velocity, v is linear velocity, and r is the radius of the circle.

3. How do I find the angular velocity of an object?

To find the angular velocity of an object, you need to know the object's linear velocity and the radius of the circle through which it is moving. You can then use the formula ω = v/r to calculate the angular velocity in radians per second (rad/s) or degrees per second (deg/s).

4. What is the difference between angular velocity and rotational speed?

Angular velocity and rotational speed both measure the rate of rotation of an object, but angular velocity takes into account the direction of rotation, while rotational speed does not. Angular velocity is also measured in radians per second (rad/s) or degrees per second (deg/s), while rotational speed is measured in revolutions per minute (RPM) or revolutions per second (rps).

5. How can I use angular velocity to find the velocity of an attached block?

If a block is attached to a rotating object, the block will have the same angular velocity as the object. You can then use the formula v = ωr, where v is linear velocity, ω is angular velocity, and r is the distance from the center of rotation to the block, to calculate the velocity of the attached block.

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