0.33 Phy1330: angular momentum -- torque, work and energy  (Page 2/4)

The machine fights back

However, the machine fights back and the compression in the cylinders creates a resistive torque. Ifthe user pulls hard enough, the torque created by the user overcomes the resistive torque, the pulleyturns, the parts inside the engine move appropriately, and hopefully the engine starts running.

When the engine refuses to start...

Clearly when the engine refuses to start, it becomes apparent very quickly that torque can do work on a human. A few dozen pulls on the rope will cause even the mostphysically fit user to become exhausted.

The force does the work

The textbook point out that it is actually the force and not the torque that does the work. However, torque and force are related in a very definitive way,and the textbook points out that it is often easer to calculate the amount of work done on the basis of torque rather than making the calculation on the basisof force.

Review -- what is work?

You learned in an earlier module on translational motion that the work done by a constant force is the product of the force and the displacement caused bythat force. In other words,

Wt = Ft * d

where

• Wt represents translational work in joules or newton-meters
• Ft represents translational force in newtons
• d represents the displacement in meters

A rotational analogy

Similarly, work done by a constant torque can be calculated as the product of the constant torque and the displacement caused by that torque.

A constant torque

It is important to note that the entire remaining discussion in this section applies only to theapplication of a constant torque. I will have a few words about a variable torque in the next section .

Power

The power generated or consumed by the application of a constant torque can be calculated as the product of the constant torque and the angular velocity.

A wheel scenario

Imagine a force being applied to a point on the outer edge of a wheel to cause an angular displacement of the wheel. As you will recall from an earlier module,the torque produced by the force is equal to the product of

• the distance from the center of the wheel to the point where the force is applied and
• the component of the force that is perpendicular to a line drawn from that point to the center of the wheel.

The point moves through a circular arc

When the force causes an angular displacement of the wheel, the point at which the point is applied moves through acircular arc. The length of that circular, often referred to by s, can be measured. The work done is equal to the product of

• the length of the circular arc and
• the perpendicular component of applied force.

The work resulting from the application of the perpendicular force is given by the equation shown in Figure 1 .

Work as a function of torque

Now that we have the work as a function of the perpendicular force and the length of the arc, let's rewrite it in terms of torque and displacement.