Why Do Angular Accelerations Differ for Two Pivoted Rods of Varying Lengths?

[zhenyazh]

hi,
could some on help me understand why the following is true?
for some of them i wrote exactly what i don't understand, for others
i really have no idea

Two uniform rods are connected to a table by pivots at one end. Rod B is longer than rod A. Both are released simultaneously from an initial angle θ. Neglect air friction. NOTATION: CM = center of mass; α = angular acceleration; |ay|= size of downward acceleration.

True: αA and αB are dependent on θ.
just don't understand why.

False: |ax| of the CM initially equals 0 for both rods.
this would be false because of the centr. force right?

True: |ay| is initially equal for the CM of A and B.
that is because it is g right?
True: Just before landing, the CM of B has a greater speed than the CM of A.
why so? i found an explanation on the internet but there they comapered mgh to 0.5Iw^2
and from there proved b's speed is larger therefore the answer.
but why can i use such an equation? why do i not take into consideration the kinetic energy
of center of mass and how do i define the height here? according to the center of mass?

False: Rods A and B hit the table at the same time.

False: αA and αB are the same initially.

True: αA and αB both increase with time.

thanks

 

[Doc Al]

True: αA and αB are dependent on θ.
just don't understand why.

How do you find the angular acceleration? What's Newton's 2nd law for rotation?

False: |ax| of the CM initially equals 0 for both rods.
this would be false because of the centr. force right?

Find the initial acceleration of the CM by first finding the initial angular acceleration.

True: |ay| is initially equal for the CM of A and B.
that is because it is g right?

The initial acceleration is not g. (It's not in free fall.)

True: Just before landing, the CM of B has a greater speed than the CM of A.
why so? i found an explanation on the internet but there they comapered mgh to 0.5Iw^2
and from there proved b's speed is larger therefore the answer.
but why can i use such an equation? why do i not take into consideration the kinetic energy
of center of mass and how do i define the height here? according to the center of mass?

If you measure I from the axis of rotation, you are automatically including the KE of the center of mass. The change in gravitational PE can be measured by the change in height of the center of mass.

False: Rods A and B hit the table at the same time.

False: αA and αB are the same initially.

True: αA and αB both increase with time.

Figure out α as a function of θ.