Torque and rotational dynamics

In summary, the wheel initially turns at 1200 turns/min and stops in 4 min due to friction. With the addition of a supplementary torque of 300 N*m, the wheel stops in 1 min. Using the equations Torque = alpha * I and time = w/alpha, we can find the torque and moment of inertia of the wheel. With the given information, we can set up two equations and solve for the two unknowns, T (friction torque) and I (moment of inertia).
  • #1
inner08
49
0

Homework Statement


A wheel is turning initially at 1200 turns/min and stops in 4 min because of friction. If we add a supplementary torque of 300 N*m, the wheel stops in 1 min.

a) What is the moment of inertia of the wheel?
b) What is the torque of friction?


Homework Equations


Torque = alpha * I
time = w/alpha
f = ucF
Torque = -fR

The Attempt at a Solution



I figured i'd start by converting the 1200 turns/min into rad/sec

(1200 *2pi)/60 = 126 rad/sec (this gives me angular speed - w)

Then I figured i'd find the angular acceleration using the angular speed that I just found with the time it takes to stop (in this case its 4min or 240seconds).

alpha = 126/240
= 0.525

Now at first I thought I could just substitute these in the equation Torque = alpha * I but it doesn't work out.
I then realized that they are saying that there is a SUPPLEMENTARY torque and it then stops in 1min. I thought it would then be something like "initial torque + 300 = something...". Does that make any sense?

Any help to clear this up would be appreciated!
 
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  • #2
inner08 said:
Now at first I thought I could just substitute these in the equation Torque = alpha * I but it doesn't work out.
I then realized that they are saying that there is a SUPPLEMENTARY torque and it then stops in 1min. I thought it would then be something like "initial torque + 300 = something...". Does that make any sense?

Any help to clear this up would be appreciated!

You could think of it this way: [tex]M=\alpha_{1} I[/tex], and [tex]M+300=\alpha_{2} I[/tex]. The additional torque creates a new net torque, which creates a new angular deceleration. Try to work something out from here on. (P.S. Note that the moment of inertia is, of course, the same.)
 
  • #3
You are given two (related) situations with two different accelerations. Find both accelerations, then write two "Torque = alpha * I" equations. Solve both equations together and you'll get your answers.

(Oops... radou beat me to it!)​
 
  • #4
You are nearly there. Yes, Torque = alpha * I is a good equation to use.

You have got two cases. In the first one you have the unknown friction torque (call it T) and the wheel stops in 4 min. You worked out the acceleration alpha correctly.

In the second case you have an additional torque so (as you said) the torque is "initial torque + 300 = something" ... well, the "something" is just "T+300". This time the wheel stops in 1 min, so the value of alpha is different.

Using Torque = alpha * I for the two cases will give you 2 equations in the 2 unknowns (T and I) which you can solve.
 
  • #5
Thanks a bunch! I got it :)
 

Related to Torque and rotational dynamics

1. What is torque?

Torque is a measure of the turning force or rotational force on an object. It is a vector quantity, meaning it has both magnitude and direction.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied. The formula for torque is:
Torque = Force x Distance.

3. What is the difference between torque and force?

While both torque and force are measures of a type of physical interaction, torque specifically refers to the force that causes an object to rotate. Force, on the other hand, can cause both rotational and translational motion.

4. How does torque affect rotational motion?

Torque is directly proportional to the angular acceleration of an object. This means that the greater the torque applied, the faster the object will rotate. Additionally, the direction of the torque determines the direction of the rotation.

5. What is the principle of conservation of angular momentum?

The principle of conservation of angular momentum states that the total angular momentum of a system remains constant in the absence of external torque. This means that if an object's rotational motion is not influenced by an external force or torque, its angular momentum will remain constant.

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