a horizontal disk is rotating counter -clockwise about its axisof of symmetry at 14rps.Its rotational inertia with respect to its axis of symmetry is8kgm^2.A second disk,of
To calculate the moment of inertia of the second disk, we need more information about it. Specifically, we need the mass and the radius of the second disk. The moment of inertia of a disk depends on these two variables.
Once we have the mass and radius of the second disk, we can use the formula for the moment of inertia of a disk about its axis of rotation:
I = (1/2) * m * r^2
Where:
- I is the moment of inertia
- m is the mass of the disk
- r is the radius of the disk
Once we have the moment of inertia of the second disk, we can calculate its angular velocity using the formula:
ω = Δθ / Δt
Where:
- ω is the angular velocity
- Δθ is the change in angle
- Δt is the change in time
In this case, we are given the angular velocity of the first disk (14 rps). We can now use the conservation of angular momentum to find the angular velocity of the second disk.
The conservation of angular momentum states that the total angular momentum before an event is equal to the total angular momentum after the event. In this case, since only the first disk is rotating, the total angular momentum before the interaction is just the angular momentum of the first disk:
L1 = I1 * ω1
Where:
- L1 is the initial angular momentum
- I1 is the moment of inertia of the first disk (given in the question)
- ω1 is the angular velocity of the first disk (given in the question)
After the interaction, both disks will be rotating together. The total angular momentum after the interaction is the sum of the angular momentum of each disk:
L2 = I1 * ω2 + I2 * ω2
Where:
- L2 is the final angular momentum
- I2 is the moment of inertia of the second disk (which we need to calculate)
- ω2 is the common angular velocity of both disks after the interaction
Since the total angular momentum before and after the interaction is equal, we can set L1 = L2:
I1 * ω1 = I1 * ω2 + I2 * ω2
We can then solve this equation for ω2, the angular velocity of the second disk.