Answer in m/s.

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance 88 cm apart on the same axle. From the angular displacement 18.4 degrees of the two bullet holes in the disks and the rotational speed 634 rev/min of the disks, we can determinethe speed of the bullet.

What is the speed of the bullet? Answer in units of m/s.

Ok so I know I have to convert 88cm to meters which comes out to 0.88m, the 18.4 degrees to radians which comes out to 0.3211406 radians. 634 rev/min comes out to 66.3587 rad/s. I am stuck after that. If anyone can please help it would be greatly appreciated! Thanks!

Ok so I know I have to convert the 88cm distance "d" in meters which comes out to 0.88m. The 18.4 degrees incremental rotation of the two disks to radians which comes out to 0.3211406 rad. The 634 rev/min rotational speed of the two disks comes out to 66.3587 rad/sec. I am stuck after that. If anyone can please help it would be greatly appreciated! Thanks!

The time "t" to traverse the distance "d" = .88m derives from t = rad/rad/sec.

The speed V of the bullet then derives from V = d/t = .88/t.

To determine the speed of the bullet, you can use the concept of conservation of angular momentum.

The formula for angular momentum is given by L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

In this case, we need to find the angular velocity of the bullet. The angular velocity can be obtained from the angular displacement and the rotational speed of the disks.

Step 1: Convert the angular displacement from degrees to radians:
θ = 18.4 degrees
θ_radians = θ * (π/180) = 0.3211406 radians (as you have already calculated)

Step 2: Convert the rotational speed from revolutions per minute (rev/min) to radians per second (rad/s):
ω = 634 rev/min
ω_radians = ω * (2π/60) = 66.3587 rad/s (as you have already calculated)

Step 3: Determine the moment of inertia of the two rotating disks.
The moment of inertia for a disk rotating about its axis is given by I = (1/2) * m * r^2, where m is the mass of the disk and r is the radius.

Since the distance between the two bullet holes in the disks is given as 0.88 meters, the radius of each disk is r = 0.44 meters.

Now, examine the setup of the rotating paper disks and determine the mass of the disks. If the mass is not given, you will need additional information or assumptions to proceed.

Once you have the mass of the disks, you can plug the values into the formula to find the moment of inertia.

Step 4: Solve for the speed of the bullet.
The angular momentum before the bullet passes through is zero, as the disks are initially at rest.

After the bullet passes through the disks, the angular momentum is given by the bullet's angular momentum.

Therefore, we can write: L = Iω = mvR, where m is the mass of the bullet, v is the speed of the bullet, and R is the distance between the bullet holes in the disks.

Rearrange the equation to solve for the speed of the bullet, v:
v = L / (mR)

Substitute the known values into the equation to find the speed in m/s. Note: Make sure to use consistent units throughout the calculation.

Remember, you still need the mass of the rotating disks and any additional information related to the bullet in order to get the final answer.