what is the angular displacement of the wheel between t = 5 s and t = 15 s?

Given Data

• The angular displacement at $t=5s$ in the angular displacement and time graph is: ${\theta }_5=100rad$.

• The angular displacement at $t=15s$ in the angular displacement and time graph is: ${\theta }_{15}=125rad$.

(A)

The expression to calculate the angular displacement of the wheel between $t=5s$ and $t=15s$ is:

$\theta ={\theta }_{15}-{\theta }_5$

Substitute all the values in the above expression.

$\begin{array}{cc}\theta & =125rad-100rad\\ \theta & =25rad\end{array}$

Thus, the angular displacement of the wheel between $t=5s$ and $t=15s$ is $25rad$.

(B)

The expression to calculate the angular velocity of wheel at $t=15s$ is:

$\omega =\frac{{\theta }_{15}}{t_{15}}$

Here, $t_{15}$ is the time at the fifteenth second of the angular displacement and its value is $15s$.

Substitute all the values in the above expression.

$\begin{array}{cc}\omega & =\frac{125rad}{15s}\\ \omega & =8.33rad/s\end{array}$

Thus, the angular velocity of wheel at $t=15s$ is $8.33rad/s$.