Physics
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A uniform thin bar with a mass of mb and length of lb is positioned along the y-axis. The bar is capable of rotating around an axis that passes through a point a distance of b away from one of its extremities. Determine the moment of inertia of the bar relative to this axis.
A 10 kg rectangular wooden plank with dimensions 180 cm by 40 cm is used as a seesaw. What is the moment of inertia of the plank when it rotates about its centre of mass?
A 15.0 cm radius bicycle wheel has a mass of 1.5 kg. What is the moment of inertia of the wheel about an axis passing through a point on the rim of the wheel?
The linear density of a thin bar with length l b and mass m b varies with position in accordance with the function λ(y) = ay 3, where y is the distance in meters from one end of the bar and an is a constant. Determine the relationship between the constant a and the bar's mass and length.
Find the moment of inertia of a uniform solid cone about its central axis, which is the axis of symmetry perpendicular to the base. The cone has a base radius RbR_{b}Rb, height hhh, and mass mmm . Assume the cone is made of aluminum.
Hint: Consider the cone as composed of a stack of infinitesimally thin disks, each having a different radius that decreases linearly from the base to the tip as you move along the height.