What is torque?

Question

Can someone give me an equation for torque and explain how to use the equation with a given problem? The whole subject of it is confusing to me and i can't remember how to do the prolems.

Thanks
-Nick

Answer 1

Torque is a force which is applied about an axis of rotation at a distance.

Toque = Force * distance
In SI units,
Torue = Newtons * meters = N m

* It is important to note that the force here is the force which acts perpendicular to the radial distance and axis of rotation. If the applied force is not perpendicular, you must use its perpendicular component.

You can see the implication of this formula...
a small force applied at a very long radial distance can amount to a very large toque force. Example, using a long wrench to loosen a tight bolt requires less force than if one used a short wrench.

Just like with a normal force which causes an acceleration as per Newton's 2nd law,
F= ma
A torque also causes an acceleration, an "angular acceleration" since the object is moving about an axis,
T = I * alpha
Where I is the ojects rotational inertia, and alpha it the resulting angular acceleration (units of radians per second squared, radians measured the angular displacement)

A common type of example if the torque force involved in opening a door. A door rotates about the hinges and a force is applied on the door (on the door knob) at some distance away from its piviot point.

One might have a problem such as this,
If a 10 Newton force were applied to a door (with a rotational inertia of 5 kg m^2) at 1 meter away from its hinges, how long would it take to open fully (move a distance of pi / 2 radians)?
In this case, one has a force which acts as a torque to cause an angular acceleration and thus a displacement.
T = F * d = 10 N * 1 m = 10 N m
T = I * alpha = 5 kg m^2 * alpha = 10 N m
--> alpha = 2 rad/s^2
delta theta = 1/2 alpha * t^2
pi / 2 radians = 1/2 * 2 rad/s^2 * t^2
t = sqrt (pi / 2) seconds

Answer 2

Torque = r cross F
where
r is the distance vector from a point on the object (usually easiest to think of the center of mass of the object).
F is the force vector being applied.
cross means take the cross product (think of it as multiplication for now)

In words, torque is a "twist" that starts a body rotating.

Here's an example: put a book flat on your desk. now, push on the book. if you push right toward the center, the book moves but doesn't *rotate*-- so there's no torque.

If you push at one end of the book, it will spin around a bit. That spin means you've applied a torque.

In the terms of the equation, the distance from the center of the book to the point you push on is "r". How hard you push is "F". So if you push harder, you get more spin, because there was more torque. If you push at a point further from the center of the book, you get more spin because "r" is bigger (longer).

All this is the "2D" case-- both the force vector and the "r" vector are in the plane of your desk. The torque is really a vector-- in this case a vector that is perpendicular to your desktop.

So, imagine your desktop is the XY plane with the center of the book at (0,0,0). If you apply a force of 2 newtons in the +y direction, f = (0, 2, 0). And if you apply this force *at* the point (0.1, 0, 0), ie, 0.1meters from the center of the book, then your torque is:

t = (0.1, 0 , 0) x (0, 2, 0) (note the order, it matters!)
t = (0, 0, 0.2)

The direction of the torque is +Z, or straight up out of the desktop. The torque's direction is the *axis* around which the object rotates, and it's magnitude (0.2 in this case) is how strong the spin is.

Given that torque, you still don't quite know how fast the book will spin-- because a heavy book would need more torque than a light book. You have to take into account the "moment of inertia" of that book around the particular axis for the torque.

Hope that helps some.

Answer 3

The word torque applies to anyting which is trying to rotate.
If you try to looden a bolt with a wrench it is done by applying torque because you are trying to turn the bolt.
Torques is really Energy. It is equal to force time distance (the radius of rotation).So force x distance = Energy

Answer 4

the measurement of force thats in a twisting motion dont remember the equation either sorry