Torques exerted on a vertical disk by multiple forces

In summary, the problem involves finding the torque using the formula force x (distance from axis to point of application) x (sine of angle between). This can be simplified by finding either the horizontal distances from the axis to the forces or the components of the forces perpendicular to the rod. The magnitude of the torque can be calculated using the formula rFsin theta.
  • #1
paulimerci
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Homework Statement
A uniform disk is mounted to an axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk. A block is attached to the end of the rod. Properties of the rod, and block are as follows.
Rod: mass=m, length = 2R
Block: mass= 2m
Disk: radius =R The system is held in equilibrium with the rod at an angle theta 0 to the vertical, as shown in the figure, by a horizontal string of negligible mass with one end attached to the disk and the other to a wall. Determine the tension in the string in terms of m, theta 0, and g.
Relevant Equations
T = Fx R x sin ϴ
This was how the solution was arrived in the text,
Net torque = F block x d block x sin ϴ0 + F rod x d rod x sin ϴ0 - T R sin 90
0 = 2mg x 2R x sin ϴ0 + m x R x sinϴ0 - T R
T = 5 mg sinϴ0
I'm wondering do we have to resolve the forces for rod and block in to components here and find for the component which is perpendicular to the vertical. I'm confused could anyone help me.
 

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  • #2
As the probem gives you R, yes, you are forced to determine the vertical component of weight.
 
  • #3
Lnewqban said:
As the probem gives you R, yes, you are forced to determine the vertical component of weight.
Lnewqban said:
As the probem gives you R, yes, you are forced to determine the vertical component of weight.
Is the vertical component sin theta here, can anyone explain how?
 
  • #4
I mean is the perpendicular component here is sin theta?
 
  • #5
paulimerci said:
do we have to resolve the forces for rod and block in to components here and find for the component which is perpendicular to the vertical.
The formula is force x (distance from axis to point of application) x (sine of angle between).
Equivalently, either
force x (perpendicular distance from axis to line of application), or
(component of force perpendicular to distance from axis to point of application) x (distance from axis to point of application).
So in the present case you can either find the horizontal distances from axis to forces or find the components of the forces normal to the rod.
 
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  • #6
Please study the diagram below. There is a position vector ##\mathbf{r}## and force vector ##\mathbf{F}.## Then there is component ##r_{\perp}## perpendicular to the line of action of ##\mathbf{F}## and component ##F_{\perp}## perpendicular to the direction of ##\mathbf{r}.## The magnitude of the torque is
$$\tau=rF_{\perp}=r_{\perp}F=rF\sin\theta.$$There is nothing more to it. Draw the dotted lines either along the forces or along the positions and figure it out.

TorqueDefinition.png
 
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What is a torque?

A torque is a measure of the force that causes an object to rotate around an axis or pivot point. It is calculated by multiplying the force applied to an object by the distance from the pivot point to the point where the force is applied.

How do multiple forces affect the torque exerted on a vertical disk?

When multiple forces act on a vertical disk, the resulting torque is the sum of all the individual torques. This means that the direction and magnitude of each force, as well as the distance from the pivot point, must be taken into account when calculating the total torque.

What is the difference between clockwise and counterclockwise torque?

Clockwise torque is when a force causes an object to rotate in the same direction as the hands of a clock, while counterclockwise torque is when a force causes an object to rotate in the opposite direction. The direction of the torque depends on the direction of the force and the distance from the pivot point.

How is torque related to angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes. Torque is directly proportional to angular acceleration, meaning that a larger torque will result in a greater angular acceleration. This relationship is described by the equation: torque = moment of inertia * angular acceleration.

What factors affect the stability of a vertical disk under multiple forces?

The stability of a vertical disk under multiple forces depends on the magnitude and direction of the forces, as well as the distance between the forces and the pivot point. A larger distance between the forces and the pivot point will result in a more stable disk, while a smaller distance will make the disk more prone to tipping over.

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