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Torque
Torque
Torque is the rotational equivalent of a force. It is a measure of the effectiveness of a force in changing or accelerating a rotation (changing the angular velocity over a period of time). In equation form, the magnitude of torque is defined to be:
𝛕 = r⟂F
𝛕 = rF sin θ
Where 𝛕 (the Greek letter tau) is the symbol for torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the vector directed from the point of application to the pivot point
Equilibrium - Two Conditions
Equilibrium - Two Conditions
Condition 1:
Condition 1:
The net external force on the system must be zero. Expressed as an equation, this is simply:
𝚺F = 0
Note that if net force is zero, then the net external force in any direction is zero. For example, the net external forces along the typical x- and y-axes are zero. This is written as:
𝚺Fx = 0 and 𝚺Fy = 0
Condition 2:
Condition 2:
The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (i.e. maintaining a constant angular velocity).
A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it.
The second condition necessary to achieve equilibrium:
Σ𝛕 = 0
Torques, which are in opposite directions are assigned opposite signs. A common convention is to call counterclockwise (ccw) torques positive and clockwise (cw) torques negative.
Torque Exploration
Torque Exploration
Hammer of Sierra Madre
Hammer of Sierra Madre
Two prospectors searching the Sierra Madre find a golden sledge hammer. After encounters with bandits, and other trials, they must divide the gold into two equal shares. They decide to do this by balancing the hammer at a point on the handle, and cutting the sledge in two right at the balancing point. Sketch the scenario when it is in equilibrium.
Identify the pivot point. Mark this point with a ^.
Identify the forces (F) and their locations (r) acting on the 'Hammer'. Hint: There are three forces, and therefore three torques.
Identify the torques acting on the 'Hammer'
Did they divide the 'Hammer' fairly?
Wrenches and Screwdrivers
Wrenches and Screwdrivers
Examine the various wrenches, screwdrivers.
Wrenches:
Sketch how a wrench would be used to tighten a bolt.
Identify the forces (F) and their locations (r) acting on the wrench.
Outline why different wrenches would be used in various situations.
Screwdrivers:
Sketch how a wrench would be used to tighten a screw.
Identify the forces (F) and their locations (r) acting on the screwdriver.
Outline why different screwdrivers would be used in various situations.
Rolling Spool
Rolling Spool
Gently pull the ribbon as shown in the diagram below.
For the three scenarios,
Identify the direction of the force and the point of rotation of the spool.
Hanging a Sign
Hanging a Sign
From the set-up of the sign suspended on the meter stick, determine the following:
The point at which the meterstick meets the support pole, There is a non-torque force acting on the system. Identify this point on your sketch. Identify the forces acting on the meterstick (often referred to as a Normal Force).
Identify the additional forces acting on the meterstick/sign system. Hint: There are three.
Santa on a Ladder
Santa on a Ladder
Suppose the top support were to break, how would Satan fall? How does this help with the discussion of Torques and forces?
How would you describe the forces acting is Satan wasn't climbing the ladder?
How would changing the angle change the torques and forces acting on the ladder?
Does the torque acting on the ladder change due to Satan's position/height on the ladder?
Between Two Ferns (Scales)
Between Two Ferns (Scales)
The mass of the meter stick is is 98.2 g. Assume the centre of mass is in the middle of the meter stick.
When two scales are put underneath, the mass is split (nearly equally) between both scales.
Determine the reading on the two scales.
He's Ducked (Stupid autocorrect)
He's Ducked (Stupid autocorrect)
The mass of the duck is 76.1 g.
Determine the mass of the meter stick.
The See-Saw
The See-Saw
What is the unknown mass?
What is the upwards normal force of the pivot acting upon the meter stick/masses?
Example 1: Balanced on a SeeSaw (stick)
Example 1: Balanced on a SeeSaw (stick)
Jimmy (right) and Wendy (left) climb on a seesaw with negligible mass. Wendy has a mass of 26.0 kg and sits 1.60 m from the pivot. Jimmy has a mass of 32.0 kg.
(a) How far is Jimmy from the pivot? Ans:1.3 m
(b) What is Fp , the supporting force exerted by the pivot? Ans: 580 N
Example 2: COM of Bar/Beam
Example 2: COM of Bar/Beam
A 500 g mass is placed at a point to the left of the pivot of a balanced meter stick. Take position measurements and use this to calculate the mass of the meter stick.
Example 3: Hanging a Sign
Example 3: Hanging a Sign
A uniform bar of mass m and length L extends horizontally from a wall. A supporting wire connects the wall to the bar’s midpoint, making an angle of 55° with the bar. A sign of mass M hangs from the end of the bar.
If the system is in static equilibrium and the wall has friction, determine the tension in the wire and the strength of the force exerted on the bar by the wall if m = 8 kg and M = 12 kg.
Shown below are six situations where vertically oriented circular disks have strings wrapped around them. The other ends of the strings are attached to hanging masses. The radii of the disks, the masses of the disks, and the masses of the hanging masses all vary. The disks are fixed and are not free to rotate. Specific values of the variables are given in the figures.
Rank these situations, from greatest to least, on the basis of the magnitude of the torque on the disks. That is, put first the situation where the disk has the greatest torque acting on it and put last the situation where the disk has the least torque acting on it.
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