Rotational Kinematics of a thin rod

[Cheddar]

Homework Statement

A thin rod (length = 1.50 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. (a) What is the angular speed of the rod just before it strikes the floor? (b) What is the magnitude of the angular acceleration of the rod just before it strikes the floor?

Homework Equations

No clue.

The Attempt at a Solution

radius = 1.50 m
angular displacement = 90 degrees
Any suggestion as to where to start would be great...

 

[Doc Al]

Hints:
(a) Consider energy conservation. How would you write the rotational kinetic energy of this object?
(b) What's the torque on the object?

 

[tomcue]

I would approach this problem by first identifying the known variables and using relevant equations from rotational kinematics to solve for the unknowns. In this case, the known variables are the length of the rod, the angle of rotation, and the fact that the rod starts from rest. The unknowns are the angular speed and angular acceleration just before the rod strikes the floor.

To solve for the angular speed, we can use the equation ωf = ωi + αt, where ωf is the final angular speed, ωi is the initial angular speed (which is 0 in this case), α is the angular acceleration, and t is the time it takes for the rod to rotate. Since the rod starts from rest and rotates 90 degrees, we can use the equation θ = ωi*t + 1/2*α*t^2 to solve for t. Plugging in the known values, we get t = 0.48 seconds. Substituting this value into the first equation, we get ωf = 188.5 radians/second.

To solve for the angular acceleration, we can use the equation α = (ωf - ωi)/t. Substituting in the values we just calculated, we get α = 392.7 radians/second^2.

In summary, the angular speed of the rod just before it strikes the floor is 188.5 radians/second and the magnitude of the angular acceleration is 392.7 radians/second^2. It is important to note that these values may change depending on the assumptions made and the conditions of the problem. As a scientist, it is important to clearly state any assumptions and limitations in the solution.