Question

Figure 11-28 gives the angular momentum magnitude Lof a wheel versustime t. Rank the four-lettered time intervals according to the magnitude

of the torque acting on the wheel, greatest first.

Short answer

The ranking of time intervals according to the magnitude of torque is

.${\tau }_D>{\tau }_B>{\tau }_A={\tau }_C$

Step-by-step solution

Step 1: Given data

The graph L vs t is given.

Understanding the concept of torque

The torque acting on the object is equal to the moment of force. The toque is also equal to the product of the moment of inertia and angular acceleration of the object. It can be written as the time rate of change of angular momentum of the object.

Use the concept of torque and from the given graph find angular momentum at given time intervals.

The formula is as follows:

$\tau =\frac{dL}{dt}$

WhereL is angular momentum,$\tau$is torque andtis time.

Determining therank of time intervals according to the magnitude of the torque

From the graph, see that for time intervals A and C the slopes are 0.Therefore, torques are 0 Nm.

For time interval B the slope is positive and for D slope is negative, but here, magnitudes want to be found.So, the slope of time interval D is greater than B.

From this, rank torques from the time intervals,

${\tau }_D>{\tau }_B>{\tau }_A={\tau }_C$

Therefore, torques can be ranked from the given time intervals using the concept of torque. The rank is,

${\tau }_D>{\tau }_B>{\tau }_A={\tau }_C$