Disk spinning with object on top, find net acceleration of object

In summary, the problem involves a disk spinning at an angular acceleration of 12 rad/s^2 and a small object placed 2 cm from the center. The magnitude of the net acceleration of the object after 0.25 seconds is needed. Using the tangential acceleration formula, Atang=r@, the tangential acceleration is found to be 24. To find the net acceleration, the object's stationary velocity with respect to the disk must be considered, leading to two components of acceleration that can be added together as vectors.
  • #1
azurken
15
0

Homework Statement


A disk begins spinning from rest with angular acceleration @ = 12 rad/s^2. A small object is on the disk a distance r = 2.0 cm from the center. What is the magnitude of the net acceleration of the object after a time t = 0.25s?

(alpha) @ = 12 rad/s^2
r = 2 cm
t = 0.25 s

Homework Equations


Vtang=rw
Atang=r@
Angular motion equations..?

The Attempt at a Solution


I'm not sure where to start off with this. I actually wasn't taught this with an object placed over a spinning disk. Tangential acceleration is radius times alpha which I can use the Atang formula to get 24. From there on I'm not sure how to apply this with the time it takes to find the net acceleration of the of object.
 
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  • #2
Hint: If you assume the object is stationary with respect to the disk, it has two components of acceleration. Determine them and add them as you would add any other vectors.
 

1. What is the purpose of spinning a disk with an object on top?

The purpose of spinning a disk with an object on top is to create a scenario where the object experiences a combination of rotational and translational motion, allowing us to study its net acceleration.

2. How does the presence of the object affect the disk's rotational motion?

The presence of the object on top of the disk causes a change in the disk's moment of inertia, which affects its rotational motion. This can be calculated using the formula I = MR2, where I is the moment of inertia, M is the mass of the disk, and R is the radius of the disk.

3. How can we determine the net acceleration of the object on top of the spinning disk?

The net acceleration of the object can be determined by measuring its linear acceleration using a motion sensor and its angular acceleration using a rotary motion sensor. These values can then be combined using the formula anet = alinear + aangular.

4. What factors affect the net acceleration of the object on top of the spinning disk?

The net acceleration of the object is affected by its mass, the moment of inertia of the disk, and the speed at which the disk is spinning. Friction between the object and the disk may also play a role in the net acceleration.

5. How can this experiment be applied in real-world scenarios?

This experiment can be applied in various real-world scenarios, such as studying the motion of objects on rotating platforms or understanding the forces acting on objects in amusement park rides. It can also be used to simulate the effects of centrifugal force in space exploration and to study the behavior of spinning objects in sports and games.

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