Calculating Angular Velocity and Torque of Big Ben's Hands

In summary, This conversation is about a problem involving the minute and hour hands of Big Ben, which are made of copper and gunmetal, respectively, and have specific lengths and masses. The problem asks for the angular velocity, moment of inertia, rotational energy, and angular momentum of both hands, as well as the torque on the drive shaft when the hands point to certain numbers on the clock face. The equations for these quantities are given, but the student is struggling to solve the problem and is unsure of where to start.
  • #1
dban33
11
0

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.
 
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  • #2
dban33 said:
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! :smile:

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

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!
 
  • #3


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?
 
  • #4
dban33 said:
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.
 

FAQ: Calculating Angular Velocity and Torque of Big Ben's Hands

1. How do you calculate the angular velocity of Big Ben's hands?

The angular velocity of an object is the rate at which it rotates around a fixed point. To calculate the angular velocity of Big Ben's hands, we need to know the distance from the center of the clock to the tip of the hand, as well as the time it takes for the hand to complete one rotation. We can then use the formula ω = θ/t, where ω is the angular velocity in radians per second, θ is the angle of rotation in radians, and t is the time in seconds.

2. What is the unit of measurement for angular velocity?

The unit of measurement for angular velocity is radians per second (rad/s). This unit represents the amount of rotation in radians that an object undergoes in one second.

3. How do you calculate the torque of Big Ben's hands?

Torque is the measure of the force that causes an object to rotate around an axis. To calculate the torque of Big Ben's hands, we need to know the distance from the center of the clock to the tip of the hand, as well as the force or weight acting on the hand. We can then use the formula τ = rFsinθ, where τ is the torque, r is the distance from the center of rotation, F is the force or weight, and θ is the angle between the force and the lever arm.

4. What factors affect the angular velocity and torque of Big Ben's hands?

The angular velocity and torque of Big Ben's hands can be affected by various factors such as the length of the hand, the weight of the hand, and any external forces acting on the hand, such as wind resistance. The shape and material of the hand can also impact these values.

5. Can the angular velocity and torque of Big Ben's hands change over time?

Yes, the angular velocity and torque of Big Ben's hands can change over time due to factors such as wear and tear on the clock mechanism, changes in the weight or shape of the hands, or external forces acting on the hands. Regular maintenance and adjustments can help ensure that the hands maintain a consistent angular velocity and torque.

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