Finding the speed of a bullet via device with two rotating disks

[TmrK]

Homework Statement

The device consists of two rotating disks, separated by a distance of d = 0.879 m, and rotating with an angular speed of 96.1 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 θ = 0.161 rad. From these data, determine the speed of the bullet.

Basically, I'm lost in this equation.

 

[LawrenceC]

What do you mean left disk, then right disk? How are the disks arranged? Are they both turning on the same shaft one behind the other? A sketch would be informative. Also, please show what equations you are working with.

 

[TmrK]

θ=s/r & w=Δθ/Δt & α=Δω/Δt

 

[LawrenceC]

OK, let's get started thinking about this problem.

What do you know about distance, time, and speed? How are they related mathematically?

You know how fast the disks are turning and therefore know how long it takes to make one complete revolution. You know how much the disks turned between bullet holes. You know the distance between the disks.

This data can be related to determine the speed of the bullet. Let's see how you put it all together to solve the problem.

 

[asteriatic]

I can provide a response to help you solve this problem. The key equation to use in this scenario is the formula for angular velocity, which is ω = Δθ/Δt, where ω is the angular velocity, Δθ is the angular displacement, and Δt is the time interval. We can rearrange this equation to solve for Δt, which will help us find the speed of the bullet.

First, we need to find the time interval between the bullet passing through the left and right disks. We can do this by dividing the distance between the disks (d = 0.879 m) by the speed of the bullet. This will give us the time it takes for the bullet to travel from the left to the right disk.

Next, we can use this time interval in the formula for angular velocity to solve for the speed of the bullet. Plugging in the given values, we get:

96.1 rad/s = 0.161 rad/Δt

Solving for Δt, we get Δt = 0.001675 s

Now, we can use this value for Δt in the formula for speed, which is v = d/Δt. Plugging in the values, we get:

v = 0.879 m/0.001675 s = 525.07 m/s

Therefore, the speed of the bullet is approximately 525.07 m/s. I hope this helps you understand the equation and how to solve for the speed of the bullet using the given data.