Angular Velocity: Formula for Max Velocity of Wood Block

[Brett bALL]

This is my first contact and please excuse my limited knowledge of physics.
see attached sketch.
If the steel plate is moved along the steel table in direction A at a given velocity, what is the formula for the angle to achieve maximum velocity of the wood block in direction B.

 

[chaoseverlasting]

Hi,

Im assuming that you have a basic knowledge of calculus.

If you assume that the plate moves in the direction A with a velocity v, then the block moves with a velocity $$vcos(\theta)$$ along the plank in the downward direction.

The projection of this velocity along the B and A direction is $$vcos\thetasin\theta$$ and $$vcos\thetacos\theta$$

$$V_B=vcos(\theta)sin(\theta)$$
Differentiate this expression wrt $$\theta$$ and equate to zero to get max value.

Otherwise, you can find the max value of Vb using trig.

 

[m2003]

Thank you for your question. I am happy to help clarify any confusion you may have about physics concepts.

Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point. It is typically represented by the symbol ω and is measured in radians per second. In the context of your question, the angular velocity of the wood block would refer to how quickly it rotates around a fixed point as it moves along the steel table.

To determine the maximum velocity of the wood block in direction B, we need to consider the relationship between linear velocity and angular velocity. Linear velocity, represented by the symbol v, is the rate of change of an object's position over time. In other words, it is how fast an object is moving in a straight line. The formula for linear velocity is v = ωr, where r is the distance from the object to the fixed point it is rotating around.

In this case, the steel plate is moving at a given velocity in direction A, and the wood block is rotating around a fixed point as it moves along the steel table. To achieve the maximum velocity in direction B, the angle between the steel plate and the table must be such that the distance between the wood block and the fixed point is maximized. This would result in a larger value for r, and therefore a larger linear velocity.

The exact formula for the angle to achieve maximum velocity of the wood block would depend on the specific dimensions and setup of the system. However, in general, the angle would need to be such that the distance between the wood block and the fixed point is maximized, which would result in a larger value for r and subsequently a larger linear velocity.

I hope this helps to clarify the concept of angular velocity and its relationship to linear velocity in this scenario. If you have any further questions, please do not hesitate to ask. Keep exploring the world of physics!