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Torque Chapter 8 Section 1

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Rotational and Translational Motion The complicated motion of any object, or objects, can be described in rotational and/or translational motion. The complicated motion of any object, or objects, can be described in rotational and/or translational motion. Translational (linear) Motion – The movement that changes the position of an object. Translational (linear) Motion – The movement that changes the position of an object. Rotational Motion – The movement that cause an object to rotate around an axis. Rotational Motion – The movement that cause an object to rotate around an axis. For this section on torque, we will focus on rotational motion. For this section on torque, we will focus on rotational motion.

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Torque Produces Rotation Torque can be seen in many different areas in the real-world. Torque can be seen in many different areas in the real-world. Vehicles Vehicles Doors Doors Wrench Wrench Etc… Etc… Anything that rotates when a force is applied to the object. Anything that rotates when a force is applied to the object.

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Torque Torque – A quantity that measures the ability of a force to rotate an object around some axis. Torque – A quantity that measures the ability of a force to rotate an object around some axis.

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Torque Depends on a Force and a Lever Arm The more force applied to an object to make it rotate, the more torque is formed. The more force applied to an object to make it rotate, the more torque is formed. The longer the distance away from the axis of rotation, the more torque applied. The longer the distance away from the axis of rotation, the more torque applied. Example: Lets look at a door Example: Lets look at a door d F Axis of Rotation

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Lever Arm Lever Arm – The perpendicular distance from the axis of rotation to a line drawn along the direction of a force. Lever Arm – The perpendicular distance from the axis of rotation to a line drawn along the direction of a force. What’s better for loosening a rusty nut? What’s better for loosening a rusty nut? Your hand or a wrench? Why? Your hand or a wrench? Why?

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Torque Depends on Angle of Force The torque also depends on the angle between a force and the lever arm. The torque also depends on the angle between a force and the lever arm. The greatest amount of torque produced is when the force is perpendicular to the lever arm. The greatest amount of torque produced is when the force is perpendicular to the lever arm.

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Torque Equation T = Fd(sinθ) T = Torque - Greek Letter “tau” T = Torque - Greek Letter “tau” F = Force F = Force d = Length of lever arm d = Length of lever arm θ = The angle between the force and lever arm θ = The angle between the force and lever arm

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SI Units of Torque The SI units for torque are: The SI units for torque are: Newtonmeters Nm Standard units seen here in good old America: Standard units seen here in good old America:Footpounds

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The Sign of Torque A torque can be positive or negative depending on the direction of rotation produced by the force. A torque can be positive or negative depending on the direction of rotation produced by the force. Clockwise rotation – NEGATIVE torque Clockwise rotation – NEGATIVE torque Counter-Clockwise rotation – POSITIVE torque Counter-Clockwise rotation – POSITIVE torque

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More Than One Force If more than one force is being applied to a single lever arm, each force that produces a torque is treated separately. If more than one force is being applied to a single lever arm, each force that produces a torque is treated separately. The sum of the torques on the lever arm will give the net torque acting on the lever arm. The sum of the torques on the lever arm will give the net torque acting on the lever arm. T net = Σ T = T 1 + T 2 + … Make sure to label the correct sign to each torque Make sure to label the correct sign to each torque

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Example Problem #1 A mechanic pushes at an angle of 85 degrees on the end of a 0.30ft wrench. If the mechanic applies a force of 105N, what is the torque applied on the bolt? A mechanic pushes at an angle of 85 degrees on the end of a 0.30ft wrench. If the mechanic applies a force of 105N, what is the torque applied on the bolt?

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Example Problem Answer #1 T = 9.41 Nm T = 9.41 Nm

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Example Problem #2 Two masses are on a seesaw on opposite sides of the pivot point. On the left side of the seesaw a 15kg mass is sitting 2.5m away from the pivot point. How far away from the pivot point would a mass of 10kg be placed on the right side of the seesaw for the seesaw to be perfectly balance? Two masses are on a seesaw on opposite sides of the pivot point. On the left side of the seesaw a 15kg mass is sitting 2.5m away from the pivot point. How far away from the pivot point would a mass of 10kg be placed on the right side of the seesaw for the seesaw to be perfectly balance? 15kg 10kg d 1 = 2.5m d 2 = ?

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Example Problem Answer #2 d 2 = 3.75m d 2 = 3.75m

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