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Tangential Velocity Formula

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Last updated date: 24th Apr 2024
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Introduction



Tangential acceleration is the rate of change of velocity at a point in case of non-linear motion. It is always perpendicular to the centripetal acceleration at that point.


So, the rate of change of tangential velocity at a point in a circular orbit is called Tangential acceleration.


\[ a_{t} = \frac{dv}{dt} \]


Where \[a_{t}\] = tangential acceleration


dv = tangential velocity


dt = change in time


Tangential acceleration in terms of displacement is


\[ a_{t} = \frac{d^{2} s}{dt^{2}}\] OR \[ \frac{dv}{ds} \]


Where s = displacement


SI unit of tangential acceleration is \[m/s^{2}\]


Example:

A body accelerates uniformly on a circular path with a speed of 10 m/s to 20m/s in 4s. Calculate its tangential acceleration. 

Solution:

Given:

Initial velocity u = 10 m/s,

Final velocity v = 20 m/s,

Change in velocity dv = v – u = 20 – 10 = 10 m/s

Time taken dt = 4s

The tangential acceleration is given by at = dv / dt

= 10 / 4

= 2.5 \[m/s^{2}\].


Question: 

A body accelerates uniformly at 2 \[m/s^2\]. on a circular path with a speed of from rest. Find the speed in 4s.


Points To Remember

  • The body’s velocity is directed tangentially at any instant when an object moves in a circular path at a distance from the centre is known as tangential velocity.

  • Angular velocity is related to tangential velocity.

  • Angular velocity is ω and tangential velocity is \[ V_{t} \]

  • a line that touches a non-linear curve at only a single point is called a tangent. It represents the relationship with an equation between the coordinates “x” and “y” on a graph.

  • Tangential formulas are of three types which are as follows - 

  • \[ V_{t} = r \times \frac{d\theta}{dt} \]

  • In order to remember the formula remember the term and its meaning which are as follow-

  • \[V_{t}\] - Tangential velocity

  • r - radius of the circular path

  • ω - angular velocity

  • t - time

  • θ- angular displacement

  • Unit for Tangential velocity formula is metre per second.

  • This formula will help to calculate the tangential velocity of the moving object in a circular motion.

  • Tangential velocity is observed in many cases like the circular motion of a satellite.


Tips For Topic Preparation

  • This chapter is an important chapter in Physics so the students have to cover this topic by understanding it.

  • This topic might be difficult because this covers circular motion so the students should know what the concept means and clear the doubts in any way possible.

  • Tutors can be hired to understand the chapter, external help will be needed for solving the problems.

  • Students should keep practising to solve the problems of this topic because this will make them understand how to solve different kinds of problems regarding this topic.

  • Make proper notes for exams that can be referred to during the exams. Students can make notes by referring to the study material and the books.

  • Referring to the notes while preparing for the exams will make them remember the main points of this topic.

  • The questions given in the chapters are important so students have to practice them. Some problems are given at the end of the notes given by Vedantu, they can refer to that and practice it.

  • While practising the problems, students can make mistakes and it's normal to make mistakes as long as it is not done in exams so students are suggested to always have solution books for the questions they are solving. This will help them to track if they are doing the solutions in the correct way.

  • Students are recommended to make running notes in their classes while the teacher covers the chapter. They might give some important points which should be marked in the books. This will make it easy for the students to refer to them first during the exams’ preparation.

  • Study the chapter with friends and discuss with them, this will help them and the student to remember the topic in an easy way. It is the best way to revise the chapter.

  • Try to make a timetable so that they can complete every topic which needs to be covered for their examinations because skipping any chapter is not a good idea, they might face problems in exams if they don’t cover every topic.

  • Students can refer to the rotation of satellites and understand the topic. It is the best example regarding this topic. They can make their own questions once they understand the concept clearly.

  • Teachers might show practicals for this, so the students should be attentive while they show how the concept works because practical work always helps us to remember the concepts easily.

  • Students are also recommended to practice the solved examples given in the book because they might get an idea of how the formulas are used in order to find the correct answers.

  • Don't just cover the practical part of this topic, the theory part should also be covered and remembered, there are chances that in exams there might be some theoretical questions regarding this topic so the students need to be prepared.

  • Students can also opt for the virtual online classes in Vedantu because this will help them to understand the topic and even clear their doubts from the best teachers in Vedantu. They will be provided with the necessary study materials which will be important regarding every topic covered.

  • Students can also download the notes from the Vedantu website for free.

  • The solutions are also available on the website which can be downloaded on the mobile app or even on the laptop in PDF form.