# A string is wound around a uniform disk of radius R and Mass M. The disk is released from rest...

## Question:

A string is wound around a uniform disk of radius R and Mass M. The disk is released from rest with the string vertical and the top end tied to a fixed bar.

Show that ( a) the tension in the string is one-third of the weight of the disk and (b) the magnitude of the acceleration of the center of mass is 2g/3.

## Torque and Angular Acceleration:

Torque {eq}\tau {/eq} is the rotational equivalent of force. Just as a force is necessary to cause an object to accelerate, torque is necessary to give an object an angular acceleration.

In many cases, when a force is applied to an object it will also create a torque. A force that does not point directly towards (or away from) an object's axis of rotation will also create a torque. In this case, the formula for torque is:

{eq}\vec \tau = \vec r \times \vec F {/eq}

Here, {eq}\vec F {/eq} is the applied force and {eq}\vec r {/eq} is a vector running from the object's axis of rotation to the point where the force was applied. We can also write this formula without vector notation as:

{eq}\tau = rF \sin \theta {/eq}

Here, {eq}\theta {/eq} is the angle between the force and {eq}\vec r {/eq}.

Since torque is the analog of force, we can use it to create an analog of Newton's second law for rotational motion. The linear form of Newton's second law is:

{eq}F_{net} = ma {/eq}

If we replace each quantity with its rotational counterpart, we get:

{eq}\tau_{net} = I\alpha {/eq}

Here, {eq}\alpha {/eq} is the angular acceleration and {eq}I {/eq} is the moment of inertia, which measures an object's resistance to being rotated. The formula for an object's moment of inertia depends on its shape. It may be convenient to have a table of moments of inertia handy when solving physics problems.

## Answer and Explanation:

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(a) This is a Newton's second law problem, but we need to keep track of both forces and torques that act on the disk. Let's begin with force.

What...

See full answer below.

Torque in Physics: Equation, Examples & Problems

from

Chapter 3 / Lesson 13
32K

After watching this video, you will be able to explain what torque is and use an equation to calculate torque in simple situations. A short quiz will follow.