Velocity and Acceleration on a Rotating Disk?

In summary, when standing on a rotating disk and walking along a straight radial line, the linear velocity can be calculated using v=w*r and the centripetal acceleration is given by a = v^2/r. However, when moving along the radial line, the velocity is a result of vector addition and acceleration can be found by differentiating the velocity vector.
  • #1
aks_sky
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Homework Statement


If you are standing on a rotating disk which is rotating at a constant angular velocity and you walk with a speed v along a straight radial line, then what are you velocity and acceleration?


Homework Equations





The Attempt at a Solution


I just wanted to check if the linear velocity in this case will be:

v=w*r

and then the acceleration will just be the centripetal acceleration or am i understanding it wrong.
 
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  • #2
The problem says that you're moving along a straight radial line - imagine that the disk has a straight line from the circumference to the centre, and, as the disk rotates, you start at the centre and walk along this line to the edge. If you were standing in one spot on the disk, then you would have [itex]v = r \omega[/itex] and [itex]a = \frac{v^2}{r}[/itex], but in the situation described, there is an additional component. I think it should just be vector addition of velocities (in two dimensions), and acceleration would be found by differentiating the vector of velocity.
 
  • #3
cheers. i get it now
 

Related to Velocity and Acceleration on a Rotating Disk?

1. What is velocity on a rotating disk?

Velocity on a rotating disk refers to the speed at which a point on the disk is moving as it rotates around its center. It is measured in distance per unit time, such as meters per second.

2. How is velocity on a rotating disk calculated?

The velocity on a rotating disk can be calculated by dividing the circumference of the disk by the time it takes for one revolution. This is known as tangential velocity and is expressed as V = 2πr/T, where r is the radius of the disk and T is the time for one revolution.

3. Is velocity on a rotating disk constant?

No, velocity on a rotating disk is not constant. As the disk rotates, the distance between a point on the disk and the center changes, resulting in a change in velocity. The velocity at any given point is constantly changing in magnitude and direction.

4. How does the radius of a disk affect its velocity?

The larger the radius of a rotating disk, the faster the tangential velocity will be. This is because a point on the outer edge of the disk has to travel a greater distance in the same amount of time compared to a point on the inner edge of the disk.

5. What is the difference between tangential velocity and angular velocity?

Tangential velocity refers to the speed at which a point on a rotating disk is moving along its circular path, while angular velocity refers to the rate at which the disk is rotating around its center. They are related by the equation V = ωr, where V is tangential velocity, ω is angular velocity, and r is the radius of the disk.

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