What is the torque exerted on the disk by the two applied forces?

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In summary, a uniform solid disk with a mass of 28.3 kg and a radius of 0.414 m is free to rotate about a frictionless axle. Forces of 90.0 N and 125 N are applied to the disk, with the lower force producing a torque out of the page and the upper force producing a torque into the page. The net torque produced by the two forces is 89.01 N*m. Using the equation torque = I * alpha, where I is the moment of inertia and alpha is the angular acceleration, the angular acceleration of the disk can be found to be -2.68 rad/s^2. The bracket holding the disk exerts a force to the left equal to the sum
  • #1
cavery4
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A uniform solid disk with a mass of 28.3 kg and a radius of 0.414 m is free to rotate about a frictionless axle. Forces of 90.0 N and 125 N are applied to the disk, as the drawing illustrates.
http://www.webassign.net/CJ/p9-31.gif

What is the net torque produced by the two forces? (Assume counterclockwise is the positive direction.)

What is the angular acceleration of the disk?

For the first question, I thought maybe to do:
90.0 N * r + 125 * r = 89.01
That is wrong.

I know of the eqn.
torque = I * alpha
but I don't know how to use it in this problem.
 
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  • #2
The two torques are in opposition. Use the sign conventions specified to find the result. Use the net torque to find the acceleration using your last equation. Look up the moment of inertia of a disk rotating about its axis of symmetry.
 
  • #3
thank you. how can i see that the forces are in opposition? i am confused b/c the arrows are pointed in the same direction.
 
  • #4
The direction of the forces are indeed the same, but in your figure the lower force would tend to make the disk rotate counterclockwise. The upper force would tend to make the disk rotate clockwise. The bracket holding the disk would have to exert a force to the left equal to the sum of the forces pulling to the right. That force is applied to the axis of rotation and produces no torque.

Torque is technically a vector. The direction is the direction of the axis about which the torque is calculated. The torque associated with the lower force would be directed out of the page toward you. The torque associated with the upper force would be directed into the page away from you. In your problem it is sufficient to just call one of the torques positive, and one negative to recognize their opposition.
 

Related to What is the torque exerted on the disk by the two applied forces?

What is torque and how does it relate to other physics concepts?

Torque is the measure of a force's ability to rotate an object around an axis. It is closely related to other physics concepts such as force, moment of inertia, and angular acceleration.

What are the factors that affect the amount of torque on an object?

The amount of torque on an object is affected by the magnitude of the force applied, the distance between the force and the axis of rotation, and the angle between the force and the lever arm.

How can torque be calculated?

Torque can be calculated by multiplying the applied force by the distance from the axis of rotation to the point where the force is applied, and then multiplying by the sine of the angle between the force and the lever arm.

What are some real-life applications of torque?

Torque is used in many everyday objects, such as wrenches, gears, and door handles. It is also important in machines and engines, such as car engines and bicycles.

How can the concept of torque be applied to solve problems?

To solve torque problems, one must identify the forces acting on an object, determine the lever arm distance, and use the equation τ = rFsinθ to calculate the torque. The principles of equilibrium and the understanding of torque can also be used to analyze and design structures and machines.

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