Linear Velocity

Understanding any concept in physics involves decoding the definition of the terms associated. In the case of linear velocity, it thus becomes necessary to define linear and velocity individually. 

Linear velocity refers to the movement of an object along a straight line or a pre-defined axis. On the other hand, velocity implies the distance that a moving body travels in a specific direction within a particular time. Therefore, the combination of these two definitions will lead you to understand the basic concept of linear velocity. 

What is Velocity?

The term velocity can be used in various fields including physics, thermodynamics, chemistry et cetera before we go into understanding linear and angular velocity we will first define velocity as an individual term.

Velocity can be explained as a rate of change of the position of an object within a certain time limit or time range, it can be differentiated into two types, angular velocity, and linear velocity. To define velocity we will take an example so imagine driving down the road and looking down at the dashboard or any signboards as we move, the speedometer shows that the car is travelling at a speed of 65 mph, then we can say that the speed of 65 mph is the velocity, which is the rate of change of miles with respect to the hours that we see. The formula velocity equals distance divided by time can calculate an object's linear velocity. In the formula, v denotes linear velocity, d denotes distance traveled, and t denotes time.

Now coming back to its different types, the linear velocity is simply the rate of change of the position of an object that is travelling along a straight path so any object that moves has a linear velocity, on the other hand, angular velocity only applies or can be applied to objects that move on a circular path and it can also be defined as the rate of change of the angular displacement over time. angular velocity, measured in rad/s, which can also be converted into degrees, is the change in angle over time. v=rω to calculate linear velocity from angular velocity.

V = ωr, where ω equals radians per second and r is the radius.

If the rotational period is t, then \[w = \frac{2\pi}{t}\]. As a result, \[v = \frac{2\pi*r}{t}\].

Linear velocity can be experienced in day-to-day life as we see so many moving objects that have a linear velocity like a person going for a walk, drive, running, or a bike ride, there can always be a linear velocity that can be observed. Furthermore, there are times when an object may be traveling along a straight path at a given constant speed, this can be said as the object traveling at a constant linear velocity, in simple words we can say that the object’s Lena velocity is not changing and hence constant. Linear velocity, measured in m/s, is the speed in a straight line.

When we talk about a circle the connection between an arc on a circle in the angle it subtends measured in radiance allows us to define quantities related to motion on a circle and through this also we can say that objects travelling along a circular path Exhibit 2 types of velocity when is linear and the other one is angular velocity as mentioned above. In addition to this, we can also understand uniform circular motion. Uniform circular motion can define the linear velocity that measures how the arc length changes over time. 

When we talk about circular motion we also talk about the direction of line velocity now the direction of the particle Salina velocity is tangential to the circular path that we see at any given point in that circular motion. Direction plays a very important role in defining the change in characteristics, velocity is a physical vector quantity which means that it requires both magnitude and direction to get its proper definition so if there is a change in speed, direction or both, the object philosophy changes and then we say that the object is an acceleration motion or accelerating.

What is Linear Velocity? 

In the most primary sense, linear velocity definition deals with the measurement of an object’s velocity when it moves along a specific direction. Therefore, it refers to the displacement of an object with respect to time. 

However, the object has to follow a specific straight line in terms of its movement. The SI unit of linear velocity is meter per second or m/s (m s-1). 

On the other hand, the linear velocity dimensional formula is M0L1T1

Also, you should know that it is a vector quantity, which indicates it has directional nature. 

What is the Formula for Linear Velocity? 

There are no points of difference between conventional velocity and linear velocity since both are vector quantities. 

Therefore, the linear velocity formula is – ν = d/t

For instance, suppose that a moving object covers a distance of 500 meters along a straight line within 10 seconds. In that case, the linear velocity of the object is – 

ν = 500 meters/10 seconds = 50 m/s or 50 m s-1. 

Logically speaking, linear velocity also applies to an object that moves in a circular direction, following a locus. In that case, it is termed angular velocity. 

What is Angular Velocity? 

Angular velocity is primarily the ratio of the angle that an object covers within a particular amount of time. In this instance, ϴ refers to the angular displacement at which a body rotates around a fixed axis. 

The formula expressing angular velocity is, therefore – νr = r.ω, 

Where νr refers to the angular velocity, ω implies time/radians, and r stands for the radius of the travelled path. Moreover, 2π radians equal 3600 in this case. You should also know that every point of the object’s trajectory has the same angular velocity because it remains constant throughout its journey. 

Can you Solve these Linear Velocity Problems?

• Amrita runs in a single direction for 10 minutes at a constant velocity. She successfully covers 1.2 km from when she started running. What will be her linear velocity in SI units? 

• The linear velocity of a specific car along a straight highway is 150 km/h, and it travels 50 km within a specific time. How much time (in seconds and minutes) will it take the car to cover that distance? 

• A moving object X has a linear velocity of 100 m/s and travels from point A to B in 1 minute 40 seconds. What is the distance between points A and B? 

How does Linear Velocity Differ from Speed? 

Even though both velocity and speed aim to find out the distance that a moving object covers within a certain period, there are some points of difference between them.

First of all, speed is a scalar quantity. This suggests that the expression of speed in m/s or m s-1 conveys only the magnitude. It does not imply anything about the direction in which the moving object travels. Certain instances of scalar quantities are energy, mass, and time. 

On the other hand, linear velocity specifies the direction of travel. It is because velocity is a vector quantity and suggests both the magnitude and direction of the moving body. Some other examples of vector quantities are force and momentum. 

Now that you know what is linear velocity, make sure that you go through related topics to gather comprehensive knowledge on the same. Also, you can download our Vedantu app to benefit from our interactive learning experience from professionals in the field of physics.