A net torque is applied to the edge of a spinning object as it rotates about its internal axis. The table shows the net torque exerted on the object at different instants in time. How can a student use the data table to determine the change in angular momentum of the object from $ 0 $ to $ 6 $ $ \text{s} $? Justify your selection.

Time $ (\text{s}) $
Net Torque $ (\text{N} \cdot \text{m}) $

0
0

2
1.5

4
3.0

6
4.5

Question

A net torque is applied to the edge of a spinning object as it rotates about its internal axis. The table shows the net torque exerted on the object at different instants in time. How can a student use the data table to determine the change in angular momentum of the object from $ 0 $ to $ 6 $ $ \text{s} $? Justify your selection.

Time $ (\text{s}) $
Net Torque $ (\text{N} \cdot \text{m}) $

0
0

2
1.5

4
3.0

6
4.5(a) Multiply the maximum net torque by $ 6 $ $ \text{s} $, because $ \Delta L = \tau \Delta t $.
, (b) Divide the maximum torque by $ 6 $ $ \text{s} $, because $ \Delta L = \tau \Delta t $.
, (c) Create a graph of net torque as a function of time and graph four points of data by using the table. Determine the slope of the curve from $ 0 $ to $ 6 $ $ \text{s} $, because the shape of the curve on the graph will be a right triangle and the slope can be directly determined.
, (d) Create a graph of net torque as a function of time and graph four points of data by using the table. Determine the area bound by the curve and the horizontal axis from $ 0 $ to $ 6 $ $ \text{s} $, because the shape of the curve on the graph will be a right triangle and the area can be directly determined.
:

Jason · Accepted Answer

$ \boxed{\Delta L = 13.5\,\text{N\cdot m\cdot s}} $

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