How Do You Calculate Torque in a Pulley System?

In summary: Anyway, it'sT2R sin - T1R sin = I alphaIt's the torque equation for the disk, so the torque of the right object (T2R) is acting in the opposite direction to the torque of the left object (T1R). This is because the disk is rotating clockwise, so the torque from the right object is directed counterclockwise, and vice versa. It doesn't matter which object is heavier, as long as the net torque is equal to the moment of inertia (I) times the angular acceleration (alpha). In this case, theta is always 90 because the disk needs to spin in order for the system to work.
  • #1
RU2490
4
0

Homework Statement


A block of mass m1 = 2kg and a block of mass m2 = 6kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250m and M = 10kg. The fixed, wedge-shaped ramp makes an angle of 30 degrees. Coefficient of kinetic friction is .360 for both blocks. Find acceleration of the two blocks.

http://img685.imageshack.us/i/img0230oo.jpg/

Homework Equations


Net torque = I alpha
F = ma
I= 1/2 mr^2
a =r alpha

The Attempt at a Solution


I isolated the objects (3)

equation for object 1
T1-ukm1g= m1a
m1g-FN= 0

equation for object 2
m2gsintheta - T2ukm2gcostheta = m2a
FN-m2gcostheta = 0

TORQUE equation for disk
T2 R sintheta - T1 R sintheta = I alpha
I of a disk is 1/2 Mr^2 and i can also rewrite alpha as a/r so
T2 R sintheta - T1R sintheta = 1/2 Mr^2 a/r
all the R's cancel each other and theta is 90 so.
T2 - T1 = 1/2MaWhen i set all the three equation together i got the right answer of .31 m/s^2. My question is though, for the TORQUE equation of the disk why is it
T2R sin theta - T1R sin Theta = I alpha instead of
T1R sin theta - T2R sin theta - I alpha?
I don't believe it is because the system is accelerating down towards the second object since the 2nd object is heavier than the 1st(i know this is true for my force equation) Doesn't force have nothing to do with direction of torque? If you have a pulley system with two objects hanging on the sides for example.
If I call the mass on the left m1 and right m2. Is the net torque always going to be TR of right object - TR of left object? does it matter which object is heavier? this doesn't seem right.

The left object is making the disc rotate counter clock wise while the right object rotates the disk clockwise so why is it NOT TR of left object - TR of right object? isn't clockwise negative and counterclockwise positive?

also is theta always going to be 90 in case of a pulley system? since the disk has to spin so it has to be 90?

THANK YOU.
 
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  • #2
RU2490 said:
My question is though, for the TORQUE equation of the disk why is it
T2R sin theta - T1R sin Theta = I alpha instead of
T1R sin theta - T2R sin theta - I alpha?

I would say that this is the right equation:T2R sin - T1R sin = I alpha .

The disk is rotating clockwise, so the torque "I alpha" is directed counterclockwise. It's similar to the reactional force m*a which is directed opposite from the acceleration.
 
  • #3
method_man said:
I would say that this is the right equation:T2R sin - T1R sin = I alpha .

The disk is rotating clockwise, so the torque "I alpha" is directed counterclockwise. It's similar to the reactional force m*a which is directed opposite from the acceleration.

What is sin?

it will only be

T2R - T1R = Iα
 
  • #4
cupid.callin said:
What is sin?

it will only be

T2R - T1R = Iα

Formula for torque is f r sin theta. In this case Theta is 90 so it becomes t2-t1= I alpha
 
  • #5
cupid.callin said:
What is sin?

it will only be

T2R - T1R = Iα

I forgot to erase that when I quoted. My bad.
 

FAQ: How Do You Calculate Torque in a Pulley System?

What is torque and why is it important in a system?

Torque is a measure of the force that causes an object to rotate about an axis. It is important in a system because it determines the rotational motion and stability of the system. In many systems, torque is used to generate or control motion and can also be used to calculate the amount of force required to rotate an object.

How do you calculate the torque of a system?

To calculate the torque of a system, you need to know the force being applied, the distance between the force and the axis of rotation, and the angle between the force and the lever arm. The formula for torque is torque = force x distance x sin(angle). The unit for torque is Newton-meters (Nm).

What is the difference between positive and negative torque?

Positive torque causes an object to rotate in a clockwise direction, while negative torque causes the object to rotate in a counterclockwise direction. Positive torque is also known as a clockwise torque and negative torque is also known as a counterclockwise torque.

How does the distribution of mass affect the torque of a system?

The distribution of mass in a system affects the torque by changing the location of the center of mass. The center of mass is the point where the entire mass of the system can be considered to be concentrated. A system with a concentrated center of mass will have a smaller torque compared to a system with a more spread out center of mass.

How can torque be increased or decreased in a system?

Torque can be increased in a system by increasing the force applied, increasing the distance between the force and the axis of rotation, or increasing the angle between the force and the lever arm. Torque can be decreased by doing the opposite - decreasing the force, distance, or angle. Additionally, changing the distribution of mass in a system can also affect the torque.

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