Angular acceleration of a drill

[notsam]

Homework Statement

A dentist’s drill starts from rest. After 3.07 s
of constant angular acceleration, it turns at a
rate of 24400 rev/min.
Find the drill’s angular acceleration.
Answer in units of rad/s2.

Homework Equations

F=mv^2/r, vi=vf+at, a=v^2/r

The Attempt at a Solution

The part that I don't understand is how 2440 rev/min is related to the other units. If I knew this I could probably solve it.

 

[cupid.callin]

how many radians will be covered one revolution ?

just put that and use 60s for 1min .. you'get speed in rad/s

 

[notsam]

And rads/sec can be used as a velocity?

 

[boddie]

rad/s is angular velocity... 2(pi) rad = 1 rev i believe

 

[cupid.callin]

use eqn of on velocity not linear velocity to solve this question

w = w_o + αt

 

[notsam]

Thanks! This isn't part of the homework but I am curious because my teacher said that it would be on the test, what if I wanted to find the angle that the drill rotates? Since I have 24400 rev/min = 2555 rad/sec over an interval of 3.07 s, I would multiply 2555 x 3.07 which would give me radians and then convert it to degrees?

 

[cupid.callin]

all the Newton eqn's are valid for rotation in angular form

2555 x 3.07 will not work as you have acceleration

Try this:

θ = w_ot + 0.5αt²

Which come from

s = ut + 0.5at²

 

[cupid.callin]

*just use:

s = θr
v = wr
a = αr

for all Newton eqn to convert them to rotation one ! :)

 

[notsam]

No way? So when it's at rest it simplifys to s=.5at^2? And s= arc legth in radians?

 

[cupid.callin]

No way? So when it's at rest "initially" it simplifys to s=.5at^2? And s= arc legth in radians?

length cannot be in radian ... rad is a pure number .. length is in meters

 

[notsam]

Ok so the basic kinematic equation for distance can also be used for angles when using angular acceleration. That is SO helpful that just opened up a door in my mind I understand this matertial so much more now!

 

[cupid.callin]

Yes they can be
i already gave you 2

last one is : w² = w_o² + 2αθ

 

[Chronos]

2555 rads/sec is the final velocity after 3.07 seconds of constant acceleration.