What is the drill's angular acceleration?

In summary, the question is asking for the drill's angular acceleration given its initial and final angular velocities and the time it takes to come to a halt. The solution involves using the equation for angular acceleration, which does not require the radius or linear velocity.
  • #1
algorith01
3
0

Homework Statement



A high-speed drill rotating ccw at 2200rpm comes to a halt in 2.80 s. What is the drill's angular acceleration?

Homework Equations



(where w = angular velocity)
w = 2╥/T
v = wr
a = v^2/r
a = w^2*r

The Attempt at a Solution



I start by calculating w. So first I took it to rev per second and then second per revolution which came to be 0.027 seconds per revolution. So w = 2╥/0.027 = 232.71 radians. Now I'm stuck because I don't have r (radius). I've tried going backwards to get r from v, but to no success since v depends in r as r depends in v. Every equation relating to acceleration seems to need r but I don't see how I can get it. Any ideas would be appreciated. Thanks.
 
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  • #2
you don't need radius or linear velocity.

[tex]\alpha = \frac{\omega_f - \omega_i}{t}[/tex]
 
  • #3
Thank you. I realized after you posted that equation that it was a nonuniform circular motion problem, I was going about it the wrong way.
 

FAQ: What is the drill's angular acceleration?

What is the drill's angular acceleration?

The drill's angular acceleration refers to the rate at which the drill's rotational speed changes over time. It is a measure of how quickly the drill is accelerating or decelerating as it rotates.

How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed changes, while linear acceleration is a measure of how quickly an object's linear speed changes. Angular acceleration is measured in units of radians per second squared, while linear acceleration is measured in units of meters per second squared.

What factors can affect the drill's angular acceleration?

The drill's angular acceleration can be affected by a number of factors, including the torque applied to the drill, the mass and distribution of the drill's weight, and any external forces acting on the drill.

How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in the drill's rotational speed by the time it takes for that change to occur. It can be expressed as the change in angular velocity divided by the change in time, or as the product of the moment of inertia and the angular acceleration.

Why is angular acceleration important in drilling processes?

Angular acceleration is important in drilling processes because it affects the speed and efficiency of the drilling. By controlling the angular acceleration, the drill operator can ensure that the drill is rotating at the optimal speed for the specific drilling task, which can help to increase productivity and reduce wear and tear on the drill.

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