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1)A wagon wheel is constructed as shown in the figure. The radius of the wheel is 0.300 m, and the rim has mass 1.49 kg . Each of the eight spokes, that lie along a diameter and are 0.300 m long, has mass 0.220 kg.

What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel?

Ok i know that the moment of inertia of just the outer rim is MR^2 but how do i take into account the Moment of inertia of the eight spokes?

I tried treating the spokes as if they were rods and using ML^2/12 and multiplying by 8 for the eight spokes but my answer came out wrong? so how is it supposed to be?

2) A uniform, solid disk with mass

*m*and radius

*R*is pivoted about a horizontal axis through its center. A small object of the same mass

*m*is glued to the rim of the disk.

If the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when the small object is directly below the axis.

I have no idea where to begin on this any hints or tips?

3)A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate

Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F_1=18.0N, F_2=24.0N, and F_3=14.0N. The plate and all forces are in the plane of the page. Take positive torques to be counterclockwise.

Ok so i know that the effective lever arm r is perpendicular to O so for torque_1 is did T_1=18.0N*.09m=2.34 N*m and for T_2 similarly i did T_2=24N*.09m=1.62N*m but for T3 im stuck.... after i found all the individual torquest are they simply added together for net torque or must i multiply by and angle between them all?

4) A grindstone in the shape of a solid disk with diameter 0.460m and a mass of = 50.0kg is rotating at omega = 840 rev/min . You press an axe against the rim with a normal force of F = 220N, and the grindstone comes to rest in 7.00s .

Ok i thought this one was going to be easy but i was wrong. I tried using W_other=-K1 since my other works canceled out. i converted omega into rad/s and for K1 i got -5116J. W_other should be the force times the distance it was done at correct? what i did was soemthing like d=r*t but i did d=omega*t and also tried using the tangent v=omega*r to find the distance that the friciton force acts to get its work.

Anyone see where im goin wrong or have a better method on this one?