# How To Find Torque with Mass: With Problem Examples

In the present article, we will focus on how to find torque with mass.

We are already aware that it is possible to rotate an object about an axis; the torque is the force responsible for this rotation. The torque is basically responsible for the angular acceleration. The torque, in general, is associated with the rotational force that corresponds to the rotational motion about an axis.

The following part explains how to find torque with mass.

## How to find torque with mass?

Torque basically belongs to vectors. By taking the cross-product of two vectors, namely the radial distance vector and the force vector, we may get torque. We may now see how to find torque with mass, in general, a vector that we get when we take the cross-product of the radial distance vector and force vector. The vector that results, which is torque, is basically perpendicular to the vectors that are subjected to cross product, and also, the force is a product of mass with acceleration.

The next question deals with the formula associated with how to find torque with mass.

## The formula of torque with mass

The level arm is the distance measured perpendicularly from the point of the force application. We already know that force is the resultant when we multiply mass with acceleration, and further, the product of this force with radial vector achieves the torque. We take ‘r’ as the length of the lever arm, and ‘θ’ be the angle traversed by the force vector with respect to the level arm. Then, the formula that shows how to find torque with mass is,

τ = F.r.sinθ

τ = (m.a).r.sinθ ,    m-mass and a-acceleration.

Torque is basically orthogonal to the vectors involved in the cross product, and then the force is a product of mass and acceleration.

The next question deals with the formula associated with how to find torque with mass and distance.

### Problem: If the mass of the object is 10kg and acceleration is found to be 0.5 m⋅s−2, and the length of the lever arm is r=4m. Find the torque when the angle between the force vector and radius vector is 30°.

Solution: We know that, τ = F.r.sinθ

τ = (m.a).r.sinθ

we get,

τ = (10 x 0.5) x 4 x sin 30°

τ = 10 N-m

The above example shows how to find torque with mass.

The upcoming section may let you understand how to find torque with mass and distance.

## How to find torque with mass and distance?

Torque basically belongs to vectors. By taking the cross-product of two vectors, namely the radial distance vector and the force vector, we may get torque. When we place a dipole in an electric field, it is found to attain a translational equilibrium. This is basically because of the action of electric pressure on positive as well as negative charges in equal amounts along in both directions. Here we may calculate torque with the help of the expression, τ = P.E.sinθ Where, P-dipole moment and E- electric field.

Dipole moment, P=q×d where q-charge and d-distance between the charges in a dipole.

Both the force and radius are responsible for the magnitude of torque with mass.

### If the electric field intensity in which an electric dipole is kept making an angle of 30° is 3 × 104 N ⁄ C. Find the torque acting on the dipole when the charge is 0.1C, and the distance between the charges is given; to be 3.35 × 10-3m?

Ans:  Electric field, E = 3 × 104 N ⁄ C

Angle between dipole and electric field, θ = 30°

Charge = 0.1C

distance between the charges,d=3.35 × 10-3m

τ = P.E.sinθ

= (0.1×3.35× 10-3C-m)(3 × 104 N ⁄ C) sin(30°)

=5 Nm

The above example shows how to find torque with mass and distance.

The upcoming section may let you understand how to find torque with mass and radius.

## How to find torque with mass and radius?

We already know that force is the resultant when we multiply mass with acceleration, and further, the product of this force with radial vector achieves the torque. We take ‘r’ as the length of the lever arm, and ‘θ’ be the angle traversed by the force vector with respect to the lever arm. Then,

τ= F.r.sinθ

When we evaluate torque, we may witness that it gets influenced by both the magnitude of the force that is applied as well as the distance which is measured at right angles from the point of the force application.

### Problem: If the force is applied, F= 5N and the radius is r=4m. Find the torque when the angle between the force vector and radius vector is 30°.

Solution: We know that, τ = F.r.sinθ

Now, substituting the given values in the above equation, we get,

τ = 5 x 4 x sin 30°

τ = 10 N-m

The above example shows how to find torque with mass and radius.

The next part deals with frequently asked questions regarding how to find torque with mass.

## How many types of torque are there?

There are, in general, two different varieties of torque that are identified,

Static torque: A static torque may not be responsible for the generation of angular acceleration, which is usually associated with rotational motion. For example, The torque in action when a closed-door is tried to push is the static torque.

Dynamic torque: The dynamic kind of torque usually succeeds in producing angular acceleration corresponding to the rotational motion. For example, A dynamic torque can be witnessed in a drive shaft placed in a racing car.

## Explain an example involving torque?

Let us now take the very old and familiar example of a door and try to explore the concept of torque. When we try to rotate the door by applying the force at a point that is nearer to the hinge, we may find that there is an expenditure of more force when compared to that of when the force is applied at the exact center of the door.

Thus, we can see that, Both the point and direction of application of force play a vital role in deciding the amount of force required.

We would require a comparatively smaller force when the axis coincides with the point of force application and the hinge is orthogonal to the torque.

## What differentiates torque from force?

The force actually decides the magnitude of the torque, but both are two different concepts. Torque represents the counterpart of force generally when it is associated with rotational mechanics. Torque, in simple words, is the ability of the force to implement a rotation or a twist around any axis. This is how torque is related to the torque.

## What does a positive and negative torque mean?

Torque can be regarded as positive or negative on the basis of force direction. A force whose action takes place in a clockwise direction is generally associated with the positive torque. In a similar way, a negative torque corresponds to a force that has been acting in the anticlockwise direction.

## What would be the difference between the torque and the moment?

Torque is itself a peculiar case of the moment. The torque is related to the axis of rotation associated with the rotational motion. In contrast, the moment is just related to being achieved by an external force that gives rise to rotation.

## How do you explain the concept of torque in a car?

Basically, a form of force that is in accordance with the rotational or a twisting force can be identified as torque. The engines that are present in the vehicles give rise to torque when they tend to rotate about an axis. It may be taken to be the strength of the vehicle. Heavy trucks, along with a lot of loads, are made to carry out motion due to torque.

#### Summary

Torque basically belongs to vectors. By taking the cross-product of two vectors, namely the radial distance vector and the force vector, we may get torque. We may now see how to find torque with mass, in general, a vector that we get when we take the cross-product of the radial distance vector and force vector. The vector that results, which is torque, is basically perpendicular to the vectors that are subjected to cross product, and also, the force is a product of mass with acceleration.

Harshitha H N

Hi.....I am Harshitha H N. I have completed my master's in Physics from the University of Mysore with a specialization in Nuclear physics. I am well versed in the field of Latex, GAMESS software, and AVAGADRO software. I enjoy exploring new things in my free time. My article always aims to develop and bring some value to the table with relevant topics. Let’s connect through LinkedIn- https://www.linkedin.com/in/harshitha-h-n-368418249