Tangential and angular velocity and acceleration

[Panda040]

Angular veloity, tangential velocity and acceleration ect.. blahh


okay so we've gon over it is class but it still confuses me...
some of the forumal's I've remembered are
s=(theta)r (theta)=s/r

anyways I am not sue how to find the tangential velocity and angular velocity what's the difference?

do i have to find the displacement (theta) and plug it into the formula V=Wr to find tangental velocity?

please any help will do I am so lost


the kind of questions I am dealing with are the steriotypical one like

an airplane is on a 3m string (radius) spinning in a horizontal circular path makes one revolution every .51 seconds (time)

and they want to knwo the tangential velocity and the angular velocity and acceleration?

i think this applies to gravity in our other problems like with a satallite orbiting at4.50x10exp6
and they want to know force and acceleration?

 

[Mindscrape]

Okay, so imagine a record turning on a record player. As the record is turning you can definitely tell that the parts towards the center are going "slower" than at the outside. This is the velocity we are used to dealing with in every day life, the "tangential velocity." This should be more physically intuitive for you.

At the same time, let's say we stop the record player, we paint a line from the center of the record to the edge, and start the record player up again. We notice that the line as a whole takes a certain amount of time to go around the record, this is the angular velocity. Just as regular velocity is a description of the change in distance over a period in time, angular velocity is a description of the change in radians over a period of time.

For a perfect circle, we can relate tangential velocity to angular velocity by the formula $$v=\omega r$$. You don't need to know the displacement to relate the two. After all, as long as the record remains whole, we know from that line we've drawn that a spot a little bit away from the center travels as far as a spot on the edge, the angular displacement is the same. As far as the displacement goes, it's simply a matter of a ratio between the circumferences.

Hopefully that makes more sense now. If not, let the ideas marinate a bit, and then look it over again.

For your problem you should try using this equation to start with:
$$\omega = \frac{\Delta \theta}{\Delta t}$$

 

[kerimek]

Hello, it seems like you are struggling with understanding the concepts of tangential and angular velocity and acceleration. Let me try to clarify these concepts for you.

Firstly, tangential velocity is the linear speed of an object moving along a circular path. It is the rate at which an object is moving tangent to the circle. This can be calculated by dividing the distance traveled along the circle by the time it takes to travel that distance. The formula for tangential velocity is v = rω, where v is the tangential velocity, r is the radius of the circle, and ω (omega) is the angular velocity.

On the other hand, angular velocity is the rate at which an object is rotating around a fixed point. It is the rate of change of angular displacement. It is measured in radians per second (rad/s). The formula for angular velocity is ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angular displacement, and Δt is the change in time.

To find the tangential velocity, you need to know the angular velocity and the radius of the circle. You can also use the formula v = rω to find the tangential velocity.

Now, for acceleration, there is both tangential acceleration and angular acceleration. Tangential acceleration is the change in tangential velocity over time. It is calculated by dividing the change in tangential velocity by the change in time. The formula for tangential acceleration is a = Δv/Δt.

Angular acceleration, on the other hand, is the rate of change of angular velocity over time. It is measured in radians per second squared (rad/s²). The formula for angular acceleration is α = Δω/Δt.

In the example you provided about the airplane on a string, you can use the formula v = rω to find the tangential velocity, and ω = Δθ/Δt to find the angular velocity. To find the acceleration, you can use the formula a = Δv/Δt for tangential acceleration, and α = Δω/Δt for angular acceleration.

Regarding the satellite example, you can use Newton's law of gravitation (F = GmM/r²) to find the force of gravity acting on the satellite. To find the acceleration, you can use the formula a = F/m, where F is the force of gravity and m is the mass of the