Angular Collisions You want to speed up the system of rotating disks. To do this

Question

Angular Collisions

You want to speed up the system of rotating disks. To do this, you throw a ball of mass mb at the two disks that are still rotating together with the same speed. You throw the ball at the disks, and the ball follows the following trajectory as viewed from above.

Now you want to slow the system down, so you decide to throw a mud ball ( mmud = 2.07 kg ) at the system of rotating disks. The trajectory from above looks like this:

Incorrect. Tries 1/15 Previous Tries Angular Collisions Two disks are initially spinning above one another, as shown in the figure below. Both disks have the same radius, R = 2.91 m. Disk 1 has a moment of inertia I1 = 9.8 kg Wf = The mud is moving with initial speed vm = 12.7 m/s and sticks to the rim of the disk upon impact. The distance d is 1.60 m. Find the common final angular velocity of the two disks and the mud. Make your answer positive if the rotation is counterclockwise as viewed from above. w new = Now you want to slow the system down, so you decide to throw a mud ball ( mmud = 2.07 kg ) at the system of rotating disks. The trajectory from above looks like this: Psi = 73 degrees Mb = 1.73 kg Theta = 64.9 degrees Psi with respect to the normal. The ball's initial speed is v0, and its final speed is vf . What is the new angular velocity of the system of rotating disks (they still rotate together) after the collision with the ball? Use these values for the parameters: vf = 1.38 m/s v0 = 8.6 m/s theta with respect to the tangent line to the disk and rebounds at an angle The ball of mass mb approaches the disks at an angle delta Etherm = You want to speed up the system of rotating disks. To do this, you throw a ball of mass mb at the two disks that are still rotating together with the same speed. You throw the ball at the disks, and the ball follows the following trajectory as viewed from above w common = How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. Disk 1 is then dropped on disk 2, and eventually the two discs reach a common, final angular velocity. Find their final angular velocity. Let counteclockwise rotation as viewed from above be positive. W2 = -18.6 rad/s W1 = 14.3 rad/s, and disk 2 is initially spinning with angular velocity m2. Disk 1 is initially spinning with angular velocity m2. Disk 2 has a moment of inertia I2 = 12.7 kg

Explanation / Answer

Finally both disc will rotate together means with same angular velocity

Using angular momentum (Iw) conservation,

so initial angular momentum = final angular momentum

(9.8 x 14.3) + (12.7 x -18.6) = (9.8 + 12.7)w

w = - 4.27 rad/s

so disc will move with 4.27 rad/s in clockwise direction.

------------------------------------------------------------------------

Initial energy of system = I1 w1^2 /2 + I2 w2^2 / 2

= ( 9.8 x 14.3^2 / 2) + ( 12.7 x 18.6^2 / 2) = 3198.85 J

final energy of system = (9.8 + 12.7) x 4.27^2 /2 = 205.12 J

Thermal energy created = 3198.85 - 205.12 = 2993.73 J

---------------------------------------------------------

moment of inertia of disc I = MR^2 /2

9.8 = m1 * 2.91^2 /2

m1 = 2.31 kg

using angular momentum conservation for discs plus ball system,

(9.8 x 14.3) + (12.7 x -18.6) + (1.73 x 1.38 x cos64.9) = (9.8 + 12.7)w + (1.73 x 8.6 x cos73)

w = - 4.42 rad/s

-------------------------------------

now using angular momentum conservation again,

(9.8 + 12.7) x -4.42 + ( -2.07 x 12.7 x 1.60) = ( 9.8 + 12.7 + (2.07 x 2.91^2))w

w =- 3.53 rad/s

(minus sign indicates the direction as clockwise direction)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.