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That is correct.Jacobs said:Is that right?
Not all parts of the pulley are at distance r from the axis.Jacobs said:But why 1/2mr^2 instead of mr^2?Yes it is cylinder but particle moves as x and y-axis not z
Yes, but only its periphery is at distance r from the axis. A mass element dm on the oeriphery does have moment of inertia dm r2 about the axis. Other parts of it are closer to the axis so have a smaller moment of inertia. The average turns out to be the same as if all parts were r/√2 from the axis. Dr dr news has posted the details of that.Jacobs said:But r is radius of pulley
The tension of a rope is an important factor to consider in many mechanical systems. It helps determine the amount of force that the rope can withstand before breaking, and also affects the movement and stability of objects connected by the rope.
The tension of a rope is directly related to the mass of a pulley. As the mass of the pulley increases, so does the tension in the rope that is connected to it. This is because the weight of the pulley adds to the overall force that the rope must support.
To calculate the tension of a rope, you will need to know the mass of the pulley, the acceleration due to gravity, and the angle at which the rope is being pulled. These variables are necessary to use the formula T = m*g*sinθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle.
Besides the mass of the pulley, other factors that can affect the tension of a rope include the length and thickness of the rope, the type of material the rope is made of, and any external forces acting on the rope. These factors may change the overall force being applied to the rope and therefore impact the tension.
The tension of a rope is a crucial factor in a variety of real-world applications, such as elevators, cranes, and rock climbing equipment. It helps determine the maximum weight that can be lifted or supported by the rope, and also ensures the safety and stability of the system.