You want to speed a system of rotating disks. To do this, you throw a ball of ma

Question

You want to speed a 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 w = -4.852 rad/s (clockwise in this problem will be negative). You throw the ball at the disks, and the ball follows the following trajectory as viewed from above.

You want to speed a 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 w = -4.852 rad/s (clockwise in this problem will be negative). You throw the ball at the disks, and the ball follows the following trajectory as viewed from above. omega new = ? Psi = 70.7 degrees mb = 1.14 kg theta = 63.6 degrees theta 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 = 2.94 m/s v0 = 17.3 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

Explanation / Answer

vf = 2.94 m/s

vo = 17.3 m/s

theta = 63.6 deg

phi = 70.7 deg

mb = 1.14 kg

Initial angular momentum of the ball ,Lbi = mb*v0*cos(theta)*r

where r = radius of the discs

Final angular momentum of the ball, Lbf = mb*vf*sin(phi)*r

Initial angular momentum of the discs, Ldi = I*Wi

where Wi = -4.852 rad/s

I= moment of inertia of discs = 0.5*M*r^2

Let the final angular speed be , Wf

So, Final angular momentum of discs, Ldf = I*Wf

So, By conservation of angular momentum,

Lbi + Ldi = Lbf+Ldf

So,  mb*v0*cos(theta)*r + I*Wi = m*vf*sin(phi)*r + I*Wf

So, mb*r*(v0*cos(theta) - vf*sin(phi)) = I*(Wf-Wi)

NOTE : To solve this question, the mass and radius of the discs needs to be given.. As you have not provide the same,I have derived the equation using them as variable.Just plug in the values to get your answer of Wf

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