An object is formed by attaching a uniform, thin rod with a mass of mr = 6.85 kg and length l = 5.76 m to a uniform sphere with mass ms = 34.25 kg and radius r = 1.44 m. note ms = 5mr and l = 4r. 1) what is the moment of inertia of the object about an axis at the left end of the rod?
kg-m2
2) if the object is fixed at the left end of the rod, what is the angular acceleration if a force f = 460 n is exerted perpendicular to the rod at the center of the rod?
rad/s2
3) what is the moment of inertia of the object about an axis at the center of mass of the object? (note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)
kg-m2
4) if the object is fixed at the center of mass, what is the angular acceleration if a force f = 460 n is exerted parallel to the rod at the end of rod?
rad/s2
5) what is the moment of inertia of the object about an axis at the right edge of the sphere?

Part a)

Part b)

Part c)

Part 4)

angular acceleration will be ZERO

Part 5)

Explanation:

Part a)

Moment of inertia of the system about left end of the rod is given as

So we have

Part b)

If force is applied to the mid point of the rod

so the torque on the rod is given as

now angular acceleration is given as

Part c)

position of center of mass of rod and sphere is given from the center of the sphere as

so moment of inertia about this position is given as

so we have

Part 4)

If force is applied parallel to the length of rod

then we have

so angular acceleration will be ZERO

Part 5)

moment of inertia about right edge of the sphere is given as

so we have

pecialized keyboards

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft