# Tangential and angular velocity and acceleration

• Panda040
In summary, angular velocity and tangential velocity are two different ways of measuring the rotation of an object. Tangential velocity is the linear speed at a certain distance from the center of rotation, while angular velocity is the change in radians over a period of time. These two velocities can be related through the formula v=\omega r, and displacement is not necessary to calculate this relationship. For problems involving tangential velocity and angular velocity, the equation \omega = \frac{\Delta \theta}{\Delta t} can be used to start solving for the unknown values.
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?

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.

$$\omega = \frac{\Delta \theta}{\Delta t}$$

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

## 1. What is the difference between tangential and angular velocity?

Tangential velocity is the linear speed at which an object moves in a circular path, while angular velocity is the rate at which an object rotates around a fixed axis. Tangential velocity is measured in units of distance per time, such as meters per second, while angular velocity is measured in units of angular displacement per time, such as radians per second.

## 2. How are tangential and angular velocity related?

Tangential velocity and angular velocity are related by the radius of the circle. The tangential velocity is equal to the angular velocity multiplied by the radius of the circle. This means that as the radius of the circle increases, the tangential velocity also increases, and vice versa.

## 3. What is tangential acceleration?

Tangential acceleration is the change in tangential velocity over time. It is caused by a change in the direction or magnitude of the tangential velocity, and is always directed tangentially to the circular path. Tangential acceleration is measured in units of distance per time squared, such as meters per second squared.

## 4. How is tangential acceleration related to angular acceleration?

Tangential acceleration and angular acceleration are related by the radius of the circle, similar to tangential and angular velocity. Tangential acceleration is equal to the angular acceleration multiplied by the radius of the circle. This means that as the radius of the circle increases, the tangential acceleration also increases, and vice versa.

## 5. What is the difference between tangential and radial acceleration?

Tangential acceleration is the change in tangential velocity over time, while radial acceleration is the change in the magnitude of the radial velocity over time. Tangential acceleration is always directed tangentially to the circular path, while radial acceleration is always directed towards or away from the center of the circle. Tangential acceleration is caused by changes in the direction or magnitude of the tangential velocity, while radial acceleration is caused by changes in the magnitude of the radial velocity.

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