Moment of Inertia and torque?

In summary, the combination of an applied force and a frictional force produces a constant total torque of 39.9Nm on a wheel rotating about a fixed axis. The applied force acts for 4.5s, during which time the angular speed of the wheel increases from 3 rad/s to 12 rad/s. The applied force is then removed and the wheel comes to rest in 72s. The moment of inertia of the wheel is 19.95 kgm^2 and the magnitude of the frictional torque is 2.49375 Nm. To find the total number of revolutions of the wheel, you must first find the total angle of rotation during the acceleration and deceleration parts, then add them
  • #1
miamirulz29
62
0

Homework Statement


The combination of an applied force and a frictional force produces a constant total torque of 39.9Nm on a wheel rotating about a fixed axis. The applied force acts for 4.5s, during which time the angular speed of the wheel increases from 3 rad/s to 12 rad/s. The applied force is then removed. The wheel comes to rest in 72s.
A. What is the moment of inertia of the wheel? Answer in units of kgm^2
B. What is the magnitude of the frictional torque? Answer in Nm
C. What is the total number of revolutions of the wheel?


Homework Equations


[tex]\sum[/tex][tex]\tau[/tex] = I(moment of inertia) * [tex]\alpha[/tex]



The Attempt at a Solution


A. 39.9 = 2I
I = 19.95
That is correct.
B. T = (19.95)(9/72) = 2.49375
That is incorrect. What am I doing wrong?
C. I need some help, do not know where to start.
Thanks in advance.
Sorry if the equations look bad. This the first time I am using Latex and I still don't know exactly how to use it correctly.
 
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  • #2
Well I just I figured out Part b. Instead of doing 12-3/72, I had to do 12/72. Can somebody explain that to me please.
 
  • #3
miamirulz29 said:
Well I just I figured out Part b. Instead of doing 12-3/72, I had to do 12/72. Can somebody explain that to me please.

You need to consider the part of the motion when only the frictional torque is acting. The wheel then slows down from 12 rad/s to 0 rad/s in 72 sec. This is why you need to divide 12 rad/s by 72 s to get alpha
 
  • #4
Oh right, thank you. Any help for part C? Just a way for me to get started please.
 
  • #5
miamirulz29 said:
Oh right, thank you. Any help for part C? Just a way for me to get started please.

You're welcome.

First you need to find the total angle of rotation during the acceleration part and during the deceleration part (you must have seen the formula [itex] \theta = \omega_i t + 1/2 \alpha t^2[/itex]). Then add the two angles for the total angle and fivide by 2 Pi to get the number of revolutions
 
  • #6
So could I do this: theta = (1/2)(12/72)(72^2) for the decelerating part and for the accelerating part could I use the other formula: 12^2 - 9^2 / 2(12-3/4.5). Then add those together and divide by 2pi?
 
  • #7
miamirulz29 said:
So could I do this: theta = (1/2)(12/72)(72^2) for the decelerating part and for the accelerating part could I use the other formula: 12^2 - 9^2 / 2(12-3/4.5). Then add those together and divide by 2pi?

For the decelerating part, you are missing one term since omega_i is not zero.

For the accelerating part, it sounds good except that you mant 3^2 instead of 9^2.
 
  • #8
Yes I meant 3^2 instead of 9^2. But isn't omega_i zero because is it come to rest when it decelerates.
 
  • #9
miamirulz29 said:
Yes I meant 3^2 instead of 9^2. But isn't omega_i zero because is it come to rest when it decelerates.

It comes to rest at the end of the decelarating part so omega final is zero. But when it started decelarating, its omega was 12 rad/s, so that's the value of omega_i for the decelerating pat
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in rotational motion. It is often referred to as the rotational equivalent of mass.

2. How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. The equation for moment of inertia is I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

3. What is the relationship between moment of inertia and torque?

Torque is the force that causes rotational motion, and moment of inertia is the measure of an object's resistance to rotational motion. The greater the moment of inertia, the more torque is required to produce the same amount of rotational acceleration.

4. How does moment of inertia affect an object's rotational motion?

The moment of inertia of an object affects its rotational motion by determining how easy or difficult it is to change the object's rotation. Objects with a higher moment of inertia require more torque to rotate, and thus have a slower rotational motion.

5. What factors affect the moment of inertia of an object?

The moment of inertia of an object is affected by its mass, the distribution of its mass, and the distance of the mass from the axis of rotation. Objects with more mass, or with mass farther from the axis of rotation, have a higher moment of inertia.

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