Calculating Angular Velocity and Torque of Big Ben's Hands

[dban33]

Homework Statement

The minute hand of big ben is made of copper, has a length of 4.27 meters, and a mass of 101.6kg. The hour hand is made of gunmetal, has a length of 2.74m, and a mass of 304.8kg. Assume that each hand is a uniform rod and rotates about one end. Use a cartesian coordinate system with +x to the right, +y up, and +z out of page. Find the angular velocity, the moment of inertis, the rotational KE, and the angular momentum of the minute and hour hand. Then calculate the torque of the drive shaft owing to the weight if the hand acting at its center of mass when the arm points to the numbers 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Torque=R x F AT There should be 34 answers in all.

Homework Equations

I don't know where to start with this problem because I don't know which equations to use.
Angular velocity= delta theta/ delta time??
moment of inertia= mr squared ((g Tm squared/ 2h) -1)?
rotational KE= theta final-theta initial/ tfinal- tinitial?

The Attempt at a Solution

My attempt at a solution failed because I do not think the equations are correct. I have been trying this problem for a week and can not figure it out. I do not even know where to start from.

 

[tiny-tim]

I don't know where to start with this problem because I don't know which equations to use.
Angular velocity= delta theta/ delta time??
moment of inertia= mr squared ((g Tm squared/ 2h) -1)?
rotational KE= theta final-theta initial/ tfinal- tinitial?
…
My attempt at a solution failed because I do not think the equations are correct.

Hi dban33!

(have a theta: θ and an omega: ω and a delta: ∆ and a squared: ² )

Angular velocity = ∆θ/∆t

Angular momentum = Iω

Rotational energy = (1/2)Iω²​

Moment of inertia (I) is only mr² for a point mass.

For something spread-out like a disc or a bar, you have to calculate the m.i. using calculus … or just look it up in a book!

 

[dban33]

Ok so I had the angular velocity correct but I do not have time to put into the equation. For the angular momentum what are I and ω?? Also, for the torque equation Torque= R x F AT...what do all of those letters mean?

 

[tiny-tim]

Ok so I had the angular velocity correct but I do not have time to put into the equation. For the angular momentum what are I and ω?? Also, for the torque equation Torque= R x F AT...what do all of those letters mean?

I is moment of inertia.

ω is angular velocity.

Torque = distance (R) "cross" force (F).

I don't know what AT means … I expect it's a misprint.