Torque equations:

$\overline{){\mathit{\Sigma}}{\mathit{\tau}}{\mathbf{=}}{\mathit{\alpha}}{\mathit{I}}}$ where I is the moment of inertia.

$\overline{){\mathit{\tau}}{\mathbf{=}}{\mathit{r}}{\mathit{F}}}$

Relationship between linear and angular acceleration:

$\overline{){\mathbf{\alpha}}{\mathbf{=}}\frac{\mathbf{a}}{\mathbf{r}}}$

Moment of inertia of a disk(pulley):

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{r}}}^{{\mathbf{2}}}}$

Uniform accelerated motion (UAM) equations:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

We'll determine the value of the linear acceleration and apply kinematics to solve for **t**.

Take the T_{1} to be the tension in left rope and T_{2} to be the tension in the right rope. T_{1} creates counterclockwise torque on the pulley while T_{2} creates clockwise torque on the pulley. The pulley rotates counterclockwise, meaning that the torque due to friction is clockwise.

The two blocks in the figure(Figure 1) are connected by a massless rope that passes over a pulley. The pulley is 12cm in diameter and has a mass of 2.7kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.50N/m.

If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Torque & Acceleration (Rotational Dynamics) concept. You can view video lessons to learn Torque & Acceleration (Rotational Dynamics). Or if you need more Torque & Acceleration (Rotational Dynamics) practice, you can also practice Torque & Acceleration (Rotational Dynamics) practice problems.