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Homework Statement. "An automobile wheel and tyre are suspended in the horizontal plane by a vertical steel rod 5mm in diameter and 2m long, which is bolted to the wheel axis. The wheel is given a small angular deflection, and makes 10 oscillations in 30.2s. Calculate the polar moment of intertia of the wheel and rod. Assume G = 80 GNm -2.
ΣM = m1*d1² + … + mn*dn² = 200kg * (1’5m)²+50kg* (0’8m)²= 482kgm². After this calculation we can see that the polar moment of inertia is 10 times higher in this case, due solely to the position of the engine since the rest of the values are identical in both examples.
In summary, the polar moment of inertia in a rod is calculated using the formula I = ∫ r^2 dm, where dm is the elemental mass and r is the distance from the axis of rotation. This formula is also known as the area moment of inertia. When dealing with a solid cylinder, the formula for mass moment of inertia is used, which is I = (M/L) ∫ r^2 dr.
The polar moment of inertia determines how easily an object can rotate around a specific axis. A larger polar moment of inertia means it will be more difficult to rotate the object, while a smaller polar moment of inertia means it will be easier to rotate. How is the polar moment of inertia used in engineering and design? The polar moment of ...
The given dimensions are: a=21'',b=9'',P=1.5''. (8 pts) Moment of Inertia. For the cross - section shown, calculate the moments of inertia and the radius of gyration with respect to both centroidal axes (X - X, Y - Y), and the polar moment of inertia with respect to an axis perpendicular to the plane of the area through its centroid.
There are 2 steps to solve this one. Solution. 100% (4 ratings) Share Share. Answered by. Mechanical engineering expert. Step 1. (a)Determine by direct integration the polar moment of inertia of the annular area shown with respec... View the full answer Step 2.
Saved Help Save & Exit Submit Check my work Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P. y 2a 2 y=c+k2x2 y=kjx r The polar moment of inertia (Jp) of the shaded area shown with respect to Point Pis The polar radius of gyration (kp) of the shaded area shown with respect to Point Pis a. < Prev 6 of 8 Next > PHY-212 Q1.png ...
5. How does the polar moment of inertia affect an object's rotational motion? The polar moment of inertia affects an object's rotational motion by determining the amount of torque needed to produce a certain amount of angular acceleration. Objects with a higher polar moment of inertia require more torque to rotate at the same speed as objects ...
Step 1. given. I x = Moment of inertia OAB about x-axis - Moment of inertia OCED x-axis. I x 1 = (A B) (D F 3) 4 = (0.75 h × 2) h 3 4 = 0.375 h 4. View the full answer Answer. Unlock. Previous question Next question. Transcribed image text: Appendix A, Practice Problem A/09 Determine the moments of inertia of the shaded area about the x- and y ...
Step 1. Take elemental section. elemental area ( d A) = r d r d θ. polar moment of inertia of a circular section ( J o) = ∫ ∫ r 2 d A. View the full answer Answer. Unlock. Previous question Next question. Transcribed image text: (6 pts) Derive the equation for the polar moment of inertia of a circular cross section with a radius of R about ...