How Does Torque Affect Angular Acceleration in a Circular Disk?

In summary, the conversation discusses the calculation of moment of inertia, torque, and angular acceleration using various equations and values such as mass, gravity, radius, and angle. The correct value for torque is determined to be 1.32 N*m based on the use of a positive value for "into the page" and the right hand rule.
  • #1
ac7597
126
6
Homework Statement
Fred makes a circular disk of copper, with mass m=1.1 kg and radius R=0.96 meters. He drills a hole at the spot marked "X", which is 0.75 of the way from the center to the edge of the disk. He then suspends the disk from a nail, so that the disk is free to rotate around the nail.

What is the moment of inertia of the disk around the nail?

Fred now swings the disk by a small angle of θ=9.8 degrees, as shown in the diagram below. He holds the disk in this position.

What is the angular displacement from its original position? Provide the answer in radians, and use a positive value to mean "into the page" and a negative value to mean "out of the page."

In this position, what is the torque around the nail due to gravity? Use a positive value to mean "into the page" and a negative value to mean "out of the page."

Fred now releases the disk. It starts to swing back to its original orientation.
What is the initial angular acceleration of the disk?
Relevant Equations
torque= Force * radius * sin(theta)
moment of inertia= [(1/2)(1.1kg)(0.96)^2+ (1.1kg) (0.75*0.96)^2]= 1.08 kg*m^2
θ=9.8 degrees= 0.17 rad

torque= (mass*gravity) * radius * sin(theta)
radius= 0.17rad * 0.96m = 0.16m
torque= (1.1kg*9.8m/s^2) * 0.16m * sin(0.17rad) = 0.29 N*m

torque = inertia * angular acceleration
0.29N*m= 1.08 kg*m^2 * angular acceleration
angular acceleration = 0.27 rad/s^2
 

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  • #2
Are you posting a solution to a problem that interests you or do you have a question to ask?
 
  • #3
Hello,
the torque is incorrect for some reason.
 
  • #4
ac7597 said:
Hello,
the torque is incorrect for some reason.
Check your premises. The reason is that one of the items that goes in the torque calculation is incorrect.
 
  • #5
the radius?
Should radius= 0.96m ?
 
  • #6
ac7597 said:
θ=9.8 degrees= 0.17 rad
Did you take this instruction into account?
... use a positive value to mean "into the page"
If so, what rule did you use to determine whether it was into the page?
ac7597 said:
torque= (mass*gravity) * radius * sin(theta)
In the context of that as a general equation, what does "radius" refer to?
 
  • #7
radius is the distance from x to the origin so (3/4)*0.96m
by the the right hand rule the torque points into the page thus it is positive:
torque= (1.1*9.8) * (3/4)*0.96 * sin(0.17rad)= 1.32 N*m ?
 
  • #8
Is it -1.32N*m?
 
  • #9
ac7597 said:
radius is the distance from x to the origin so (3/4)*0.96m
by the the right hand rule the torque points into the page thus it is positive:
torque= (1.1*9.8) * (3/4)*0.96 * sin(0.17rad)= 1.32 N*m ?
Looks right.
ac7597 said:
Is it -1.32N*m?
No, I was just checking you had thought it through.
 

1. What is torque on a circular disk?

Torque on a circular disk is the measure of the turning or rotational force acting on the disk. It is a vector quantity that depends on the magnitude and direction of the force applied.

2. How is torque calculated on a circular disk?

Torque on a circular disk can be calculated by multiplying the force applied to the disk by the perpendicular distance from the axis of rotation to the point where the force is applied. The SI unit for torque is Newton-meter (N-m).

3. What factors affect the torque on a circular disk?

The torque on a circular disk depends on the magnitude and direction of the force applied, as well as the distance between the axis of rotation and the point of application. The angle at which the force is applied also affects the torque.

4. How does torque affect the motion of a circular disk?

Torque causes rotational motion in a circular disk, similar to how a force causes linear motion. The direction of the torque determines the direction of the rotation, while the magnitude of the torque determines the speed of the rotation.

5. What is the difference between positive and negative torque on a circular disk?

Positive torque causes the disk to rotate in a counterclockwise direction, while negative torque causes the disk to rotate in a clockwise direction. The direction of the torque is determined by the right-hand rule, where the fingers point in the direction of rotation and the thumb points in the direction of the torque.

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