Calculate Bullet Speed from Angular Displacement and Rotational Speed

[sweedeljoseph]

Homework Statement

A device consist of two rotating disks, separated by a distance of d = 0.85 m, and rotating with an angular speed of 95 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is \theta = 0.24 rad. From these data, determine the speed of the bullet.

Homework Equations

w=\theta/Delta t
*v=v_o+at ~ w=w_o+\omegat
*v²=v_o²+2ax ~ w²=w_o²+2\omega\theta
*x=v_ot+(1/2)at² ~ \theta=w_ot+(1/2)at²

the ones with * means i changed it to what the problem is about. means the same thing just different letters so you won't get confused i guess.

The Attempt at a Solution

well i know the formulas but when the bullet hits the first disk won't it loose some speed and same with the second thing? does it mean speed after its done hitting or what I am confused please help.

thank you!
sweedeljoseph

 

[montoyas7940]

It doesn't seem that speed lost in each impact is considered. After all you don't know anything about the material or the bullet.

You do have the amount of time that passes between impacts however. It is the angular displacement divided by the rate of angular displacement.

After calculating the time, you will have time and distance...

 

[sweedeljoseph]

so the angular displacement is .85 and the rate of the angular displacement is 95 rad/s. if i divide those two i get .009. that's the time? i just plug that into one of the equations to find distance?

 

[montoyas7940]

No, in your post you state that the angular displacement is .24 rad. Is that correct?

 

[sweedeljoseph]

oh yeah. haha i didnt see that but that's what i meant! so the answer is .002. and I am guessing that's time. just plug that into the equation to find distance? is that it?

 

[montoyas7940]

Well, think about it like this...

If it took the bullet .002 sec to travel .85m, what is the speed of the bullet in meters/sec?

 

[sweedeljoseph]

.85/.002? that would equal 425. that would be the speed of the bullet?

 

[montoyas7940]

Close, but you need to keep more precision in the intermediate step.

.24/95 = ?

The rounding error is very large.

 

[sweedeljoseph]

wait why are you using those numbers to find the speed? i thought we just solved for something else.

 

[montoyas7940]

Yes, you are correct. I didn't check your division before and find the rounding error right away. My apologies.

If you keep more precision until the end.

You would get time= .24/95 = .002526316 sec

Then .85m/time = 336.46 m/sec

sorry to confuse you...

 

[sweedeljoseph]

oh wow ok i know what youre talking about now. its ok for confusing me I am always confused in physics its great. so the problem was that easy haha i feel so stupid. i get it now.

thank you so much!