1. Torque

2. Torque What factors affect your ability to open a door? Force
Where you apply the force

3. Torque
Forces with equal strength will have different effects on a swinging door.
The ability of a force to cause rotation depends on
The magnitude F of the force.
The distance r from the pivot—the axis about which the object can rotate—to the point at which force is applied.
The angle at which force is applied.
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4. Torque units: newton-meters, (N  m)
Torque ( ) is the rotational equivalent of force. \
units: newton-meters, (N  m)
A torque that tends to rotate the object in a counter-clockwise direction is positive,
A torque that tends to rotate the object in a clockwise direction is negative.
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5. Torque
The radial line is the line starting at the pivot and extending through the point where force is applied.
The angle ϕ is measured from the radial line to the direction of the force.
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6. Torque
The radial line is the line starting at the pivot and extending through the point where force is applied.
The angle ϕ is measured from the radial line to the direction of the force.
Torque is dependent on the perpendicular component of the force being applied.
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7. Torque
An alternate way to calculate torque is in terms of the moment arm.
The moment arm (or lever arm) is the perpendicular distance from the line of action to the pivot.
The line of action is the line that is in the direction of the force and passes through the point at which the force acts.
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8. Torque The equivalent expression for torque is
For both methods for calculating torque, the resulting expression is the same:
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9. Torque
Equations:
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10. Example 7.9 Torque in opening a door
Ryan is trying to open a stuck door. He pushes it at a point 0.75 m from the hinges with a 240 N force directed 20° away from being perpendicular to the door. There’s a natural pivot point, the hinges. What torque does Ryan exert? How could he exert more torque?
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11. Example: Where should the dumbbell be lifted?
A 1.0-m-long dumbbell has a 10 kg mass on the left and a 5.0 kg mass on the right. Find the position of the center of gravity, the point where the dumbbell should be lifted in order to remain balanced.
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12. Example Problem
Revolutionaries attempt to pull down a statue of the Great Leader by pulling on a rope tied to the top of its head. The statue is 17 m tall, and they pull with a force of 4200 N at an angle of 65° to the horizontal. What is the torque they exert on the statue? If they are standing to the right of the statue, is the torque positive or negative?
Answer: The component of the force that is perpendicular to the lever arm is 4200*sin(65)=3800 N and the torque is 3800 N * 17 m = 6.5*10^5 N-m. If you are standing to the right of the statue and pulling, the statue will fall to its right which would be a counterclockwise rotation or positive torque IF the axis of rotation is defined as going forward from the face of the statue. However, if the question is interpreted as being that the force is applied to the right as seen from a third-party observer (such as a student drawing this on a piece of paper) then the torque is clockwise and negative. I think the wording of this part of this question (from the IG) is ambiguous and should be changed.
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