# Question #032b6

May 27, 2016

The net force is the vector sum of all the forces acting on an object.

#### Explanation:

Whenever a number of forces act on an object, and if the vector sum of all the forces is not balanced, then we have a resultant force. This is called net force. A net force is capable of accelerating a mass. The acceleration could be linear or circular or both.

In equilibrium state net force acting on an object is zero. The object does not accelerate.

In the figure below force $\vec{F}$ acts at a point H of a free rigid body. The body has the mass $m$ with its center of mass at point C.

The net force causes changes in the motion of the object described by the following expressions.

1. Linear acceleration of center of mass $\vec{a} = \frac{\vec{F}}{m}$;
where $\vec{F}$ is the Net Force and $m$ is mass of the object
2. Angular acceleration of the body $\vec{\alpha} = \frac{\vec{\tau}}{I}$,
where $\vec{\tau}$ is the resultant torque and $I$ moment of inertia of the body.
Torque, a vector quantity is caused by a net force $\vec{F}$ defined with respect to some reference point $\vec{r}$ as below
$\setminus \vec{\setminus} \tau = \setminus \vec{r} \setminus \times \setminus \vec{F}$
or $| \setminus \vec{\setminus} \tau | = k | \setminus \vec{F} |$