A disk of radius R rotates at angular velocity Ωinside an oil container of viscosity μ, as in Fig. Assuming alinear velocity profile and neglecting shear on the outer diskedges, derive an expression for the viscous torque on thedisk.4546

1- Force of viscosity F acting on a spherical body moving through a fluiddepends upon its velocity (v), radius (r) and coefficient of viscosity ‘η’ ofthe fluid. Using method of dimensions obtain an expression for ‘F’.

A uniform disk with mass 41.0 kgkg and radius 0.220 mm is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 29.5 NN is applied tangent to the rim of the disk.Part AWhat is the magnitude v𝑣 of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.190 revolution?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =ratnothing

The cross-section of a fluid bearing is shown below. The concentric cylinders are 10 cm in length. The innercylinder has radius 1.9 cm and is stationary whilst the outer cylinder has radius 2 cm and rotates with an angularvelocity 𝜔 = 500 rad/s. The fluid between the cylinders is S.A.E. 10 oil (density 𝜌 = 917 kg/m3 and dynamicviscosity 𝜇 = 0.104 N.s/m2).𝜔 = 500 rad/s 1.9 cm2 cm10 cmfluid in gap(a) By assuming a linear velocity profile of the fluid in the gap between the two cylinders, estimate the(resistive) torque and the power required to maintain constant angular velocity of the outer cylinder.(b) In arriving at the estimate of part (a) above, what assumptions have been made in the modelling.(c) By estimating the Reynolds number, suggest why the calculations might not be appropriate for the sameparameters except with water (density 𝜌 = 1000 kg/m3 and dynamic viscosity 𝜇 = 0.001 N.s/m2) replacingthe oil.

Question 5The chef at a pizza restaurant tosses a spinning disk of pizza dough into the air. As the disk stretches outward in midair and its diameter increases, what happens to the disk's angular momentum and angular velocity about the disk's center of mass? [Note that the disk's weight, which acts at the disk's center of gravity, produces zero torque on the disk about the disk's center of mass. Ignore any effects due to the air.]1 pointThe disk's angular velocity is constant, but the disk's angular momentum increases.The disk's angular momentum is constant, but the disk's angular velocity increases.The disk's angular momentum is constant, but the disk's angular velocity decreases.The disk's angular momentum and angular velocity are both constant.

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s–1. The value of n, to the nearest integer, is _______. [Given : In one complete revolution, the disk rotates by 6.28 rad]