Common Misconceptions

• The higher the torque, the faster a drill will complete an application. This is not always the case. Torque is the amount of force the drill produces to turn an object, not how fast an object will turn.

•  Confusion between torque and horsepower. Torque is not the factor that decides how fast a car goes up a hill, that is horsepower. More torque does not mean better pull.

• High torque does not mean, faster rotations. For example, high torque engines rotate wheels proportionally more slowly than low torque engines. But high torque engines are "cranking" harder.

Rigid-Body Statics Problem

To Solve:

1. Draw a FBD

2. Find the length of the lever arms

3. Resolve forces

4. Create a chart 

5. Set values equal to eachother and solve

Torque and Everday Life

Opening and closing doors: It is easier to do so further away from the hinges of a door, where the lever arm is longer.

Torque wrench: Applies specific torques to fasteners, such as nuts and bolts.

The amount of torque in car engines, which is transferred to tire rotation.

Fastening screws, nuts, bolts

Ladder placement

Balancing Objects

 

Free Body Diagram

Math Problems dealing with Torque

General Concept Problem

A bolt on a car engine needs to be tightened with a torque of 35Nm. You use a 25cm long wrench and pull on the end of the wrench at an angle of 60 degrees from the perpendicular. How long is the lever arm? How much force do you have to exert?


Known:

r= 0.25m
Torque= 35Nm
Θ=60

Unknown :
L= ?
F= ?

Solve for L :
L=r sin Θ
L=(0.25m)(sin 60)
L= 0.22m

Solve for F:
Torque=Force(sin Θ)
Force= Torque/r sin Θ
Force= 35Nm/(0.25m)(sin60)
Force= 1.6 x 102

See-Saw Problem

Kariann (56 kg) and Aysha (43 kg) want to balance on a 1.75c long seesaw. Where should they place the pivot point?

Known:
Mk= 56kg
M A= 43 kg
Rk + RA = 1.75m

Unknown:
Rk= ?
RA=?

Find the two forces.

Kariann:
FgK=mKg
FgK=(56 kg) (9.8 m/s2)
FgK=5.5 x 102N

Aysha:
FgA=mAg
FgA=(43 kg) (9.8m/s2)
FgA=4.2 x 102

Define Kariann’s distance in terms of the length of the seesaw and Aysha’s distance.

RK= 1.75m- rA

Where there is no rotation the sum of the torques is equal to zero.

Fgkrk=FgArA
(Fgk)rk- (FgA)rA=0Nm

Fgk (1.75m - rA) - FgArA =0Nm

Solve for rA

Fgk (1.75m) - FgK (rA) - FgArA = 0Nm
(FgK) rA+ (FgA)rA= Fgk (1.75m)
rA (FgK+FgA)= Fgk (1.75m)
rA= Fgk (1.75m)/FgK+FgA
rA= (5.5 x 102N) (1.75m) / (5.5 x 102N + 4.2 x 102 N)
rA=0.99m

Ladder Problem

What is the maximum distance x from a smooth frictionless wall you can put a 100N uniform ladder of length 5.0m on a floor where the coefficient of static friction is 0.40?




Solution: http://zebu.uoregon.edu/~probs/mech/circ/Torquilibrium3/node2.html

Important Terms

When an object is at rotational equilibrium it is not rotating or moving, during this state there is neither no net force nor torque.

The center of mass is the point of an object at which it can be suspended without tending to rotate. This is the point at which you may pretend all of the mass of an object lies, rather than acknowledge the objects distribution of mass.

In SI units, a unit of torque is measured in newton-meter. However, because torque units are force by distance this standard is not world-wide; torque can also be measured in pounds per foot.

A line of action is the direction of force. The direction of force vector will be equal to line of action vector because forces are vector quantities.

Concurrent forces occur when the lines of action of various forces have a common point preventing an object to be set into rotation. Non-concurrent forces occur when the lines of action of various forces do not intersect; this causes the object to be set into motion.

A pivot or fulcrum is the point on which a lever is free to rotate.

Mathematical fulcrum is the point that is used when solving a torque problem, such as a rigid-body static problem, where forces intersect and can also be the physical fulcrum.

Physical fulcrum is the point that an object moves about (see pivot/fulcrum above)

A couple is a pair of equal parallel forces that are opposite in direction. The torque of a couple is found by multiplying one of the forces by the perpendicular distance between them.

What is Torque?

Torque (also called momenutm or momentum of force) measures the amount of force used to rotate an object about an axis. Similarly to force, torque is a cause of an object's motion. Still, it is different because torque is dependent on force.

Torque=Force x Length of the lever arm.