Four items, all with equal masses, are used to construct the device depicted to the right. Two of the items are uniform solid disks, the smaller of which has half the radius of the other. The disks are glued together so that they share a common axle.The other two items are blocks, which are attached to (massless) ropes, each wound around a different disk, as shown in the diagram. The whole system begins at rest, with the block attached to the smaller disk starting at a lower elevation than the other block. The blocks are released and begin to fall, while the disks turn and the ropes unwind (the disks are glued together, so they turn at equal speeds at all times). Find the rotational speed of the disks (in rad/s) when the blocks reach the same height.the radius of the smaller disk is R = 0.60m, and the blocks start at a height difference

of d = 1.5m.

kindly help its urgent , i have done 24 questions this one is left i have to submit the assignment within an hour please help

To find the rotational speed of the disks when the blocks reach the same height, we can use the principle of conservation of mechanical energy.

The mechanical energy of the system is conserved as there are no external forces acting on it. The initial mechanical energy of the system is equal to the final mechanical energy of the system.

The initial mechanical energy consists of two parts: the gravitational potential energy of the blocks and the rotational kinetic energy of the disks.

The gravitational potential energy of the blocks is given by the formula:
PE = m * g * h
where m is the mass of the blocks, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the initial height difference of the blocks.

The rotational kinetic energy of the disks is given by the formula:
KE = (1/2) * I * ω^2
where I is the moment of inertia of the disks and ω is the angular velocity of the disks.

The moment of inertia of a solid disk is given by:
I = (1/2) * m * r^2
where m is the mass of the disk and r is its radius.

Since the two disks are glued together and turn at equal speeds, their rotational kinetic energy is the same. Thus, the total rotational kinetic energy of the system is twice the rotational kinetic energy of one disk.

Setting the initial mechanical energy equal to the final mechanical energy, we have:
m * g * h = 2 * (1/2) * (1/2) * m * r^2 * ω^2

Simplifying the equation, we find:
g * h = r^2 * ω^2

To find the rotational speed (angular velocity), ω, we rearrange the equation as follows:
ω = sqrt((g * h) / r^2)

Substituting the given values:
g = 9.8 m/s^2
h = 1.5 m
r = 0.60 m

ω = sqrt((9.8 * 1.5) / (0.60^2))

Calculating the value using a calculator, we find:
ω ≈ 5.12 rad/s

Therefore, the rotational speed of the disks when the blocks reach the same height is approximately 5.12 rad/s.