Linear Speed Formula

Linear speed is a topic wherein grave importance is given to formulas. You need to remember several formulas in this particular subunit. If you're unable to remember the formulas, don't worry we're here to help! Linear speed is the distance traveled by a moving object. The speed with which the object moves in a linear path is called linear speed. In simple words, we can understand that the linear speed is a distance covered by a body in a given time interval. Let us get a better understanding of what this linear speed is and also solve a few problems! 

Linear Speed Definition

The change in distance with respect to time is called linear speed. This change could be instantaneous or can be over a time frame. When the linear speed is measured over a very short interval, it is called instantaneous linear speed and when it is measured over a given time frame, it is called an average linear speed.  However, when the linear speed is measured over a concise time interval, it is more accurate.

The Formula for Linear Speed 

V(linear speed) =  \[\frac {\Delta S}{\Delta T}\]

Given above is the average linear speed formula. It is the measure of the change in linear speed with respect to time over a given time period. 

∆S represents the change in distance

And ∆T represents the time taken by the body to traverse the given distance. 

V(Linear Speed) = \[\frac {ds}{dT}\]

Given above is the formula of linear speed measured instantaneously. This measures the change in the distance within a fraction of a second of the motion. 

Here dS represents the instantaneous change in distance and dT represents the fraction of second taken for the change to occur. The instantaneous speed is more accurate since the period considered while finding the instantaneous linear speed is much lesser. 

Linear Speed Formula In Circular Motion

When a body is in a circular motion, it has two different kinds of speeds.

1. Angular speed 

2. Linear speed 

Linear speed and angular speed together constitute the speed of a body in a circular motion. Linear speed in a circular motion pushes the body to move forward whereas angular speed is caused due to the centripetal force which constrains the body to continue its motion in a circular path. The centripetal force generates an inward pull and hence manages to restrict the motion to a circular path. The linear speed is responsible for propelling the body. Without the presence of the linear speed, the circular motion will cease. Without the presence of the angular speed, the circular motion would be disrupted and the motion will continue in a tangential direction. Hence, both the components are equally important for restricting the body to a circular path.

The Angular Linear Speed

As we've seen earlier, rotational motion possesses two kinds of speeds. The angular speed of a body in rotational motion is caused due to the acceleration which drives the body forward and keeps it moving in a circular path. The formula for the angular linear speed of the is given below 

V=rw 

Where v is the linear velocity of the body and r is the radius of the circular path and w is the omega, the angular speed of the body which is moving in the circular path. 

Solved Questions 

1. A Body Starts from Rest and Moves with an Acceleration of 10 Rad s^-2 in a Circle of Radius 5m. Find the Linear Speed of the Body After 6 s.

Ans:

Acceleration a = 10 rad s^-2

Radius r =5 m

Time t = 6 s

The angular velocity is given by

ω = ω0 + at

= 0 + 10(6)

= 60 rads^-1

The linear speed is given by

v = r ω

= 5 m × 60 rad s^-1

v= 300 m/s.

Hence, the linear speed of the given body is 300m/s. That means if the centripetal force on the body is removed, the body will continue to move in a tangential direction. 

2. Find the Linear Speed of a Body Moving at 30 rpm in a Circular Path Having a Radius of 5 m?

Ans:

Given

Angular velocity  = 30 rpm

= 30 \[\frac {\pi}{30}\]

= 1 rad/s

Radius r = 2 m

The linear speed is given by

v = r ω

v = 2 m × 1 rad/s

v = 2 m/s

3. A yoyo is Rotated by a Boy in a Radius of 5m. If the Linear or Tangential Speed of the yoyo is 6 m/s, Find the Angular Speed of the yoyo. 

Ans:

Given 

R= 5m

V=6m/s

The formula for Linear Speed

v = r ω

ω=  \[\frac {v}{r}\]

ω= \[\frac {6}{5}\]

ω= 1.2

Tips to study Linear Speed Formula

Comprehending the linear speed formula was made easier through the above study content. Students must have instilled confidence in this topic. 

Preparing for such topics might be a difficult task to do for many. However, the one who unlocks the correct way to understand, apply and prepare for it can do wonders. You will always be encountered with challenges along the way. Some people tend to give up in such situations but you don't have to be one of them. You have to invest your energy in figuring out the best solution to every problem because as you move ahead, these obstacles will become much easier. Exam stress and anxiety cannot be escaped but one can surely look into things that help you calm yourself. With that, you shall also be able to do things that help you gain more confidence.

Let's get to know some of the tactics to revise a topic vividly. 

• Plan every day in advance

This technique can help you to stay focused and achieve your targets. There could be many ways that you could be doing to make your preparation easier such as making lists or following a checklist etc. Once this becomes a habit, you can take the next steps of planning out a week and even a month in advance. Make sure that you're able to pull out the proper time for each of the topics. 

• Consider the consequence

Being able to analyze and evaluate the consequences before you plan out your day or prepare yourself for any task is an important skill that the students shall possess. Answering questions like what will be its outcome or what will be the final results can help you make your study schedule more effective and efficient. 

• Focus on key result areas 

Two main areas which you should work on when you want to yield good results are working on the topics which have greater impact and working on your weaknesses. Both areas require equal time, effort and attention. Students shall make sure to align their heed and stay focused to be able to achieve what they have dreamt of.  

• Prepare yourself before you begin 

Preparing yourself before beginning is the biggest task but also a must. You may clean your surroundings and optimize your learning space. Also, don't forget to get rid of all the distractions around you. Make your environment positive and productive. Get rid of all the negative thoughts and give it a kickstart. Students shall understand that as much as it is important to put yourself at work, it is also important to prepare and boost your mental energies. 

• Motivate yourself into action 

Your inner voice forms your thoughts and emotions. Make your inner self positive and watch its power surprise you. You should not just depend on the external motivation factors and keep trying to use your energy to charge yourself. Give up on overthinking and cut the crap. Keep your spirits high and give your 100% because your efforts shall never disappoint you. 

• Get started 

This is one of the toughest tasks to do. You may be able to do all the planning but to get somewhere, it is important to push yourself to take action and that's where the real journey begins. The limiting beliefs might stop you now and then but the ones who can walk past them can achieve more than they ever thought was possible. 

Make sure that you don't rush things. Instead, your focus shall be on improvement. Everyone makes mistakes but those who fail are only the ones who refuse to try. So, make a choice wisely!