Physics circular motion equations

Circular motion is very important and interesting topic we will study here from basic concept of circular motion to the hidden concept of circular motion lets start first question what is circular motion ? answer when any body or particle moves on a circle or circular path this type of motion is called circular motion this motion is found in whole universe everywhere you can see and analyse the picture below.

                                            

  From above picture planets moves around sun in circular motion, moon moves around Earth in circular motion even electron moves in atom around the nucleus in circular path here all above examples are circular doing motion important point is heavy mass like planets Earth, Moon as well as light mass like electron are doing circular motion hence it is clear that big body as well as small particle are doing circular motion everywhere so it is very obvious if you want to understand world then important to understand circular motion so it very interesting we are going to study in this topic but at the same time from circular motion mechanics is going to some complicated so you have to understand carefully all the points in discussion as we have already studies kinematics so you can understand well circular motion because circular motion will related with kinematics you can refer Kinematics concept   you can do small question of circular motion from the concept of kinematics very easily see below questions.

                                         

   In above simple question we have just uses to answer the basic concept of kinematics which we have already studies so it is important to refer kinematics concept first then study circular motion you will understand better.

Angular variables

when an object moves on a curve its position vector always changes from reference point origin and its direction is also changes here position vector is represented by r and direction is represented by 𝜃 hence using by this two variable any particle moving on a curve path angular position can be found and this is called angular variables see below in picture.

                                           

From above picture all three case it is clear that general motion is curve motion where r position vector and angle both changes one dimensional straight line motion is special case of curve motion where angle is constant only r position vector changes  similarly  circular motion is a special type of motion where r position vector is constant only angle is changing so here we will compare in more details between one dimensional motion and circular motion so that our circular motion understanding of circular motion will more develop now see below the comparison.

                                               

                                          

   Here from above comparison between two motion we will see the below point in one dimension linear position x = +2m or x= -2 m while in circular motion angular position 𝜃 = 𝛑/3 rad or 𝜃 = -𝛑/3 rad

linear displacement 𝚫x = Xf-Xi m while in circular motion angular displacement 𝚫𝜃 = 𝜃f-𝜃i rad

linear velocity = dx/dt = v m/s while in circular motion angular velocity = d𝜃/dt = 𝛚 rad/s.

Q find 𝛚 of  second and minute hand of a clock .

it is very simple question first 𝛚 of second hands = angular displacement/time = 2𝛑/60 = 𝛑/30 rad/s now 𝛚  for minute hand = 2𝛑/60*60 = 𝛑/1800 rad/s.

linear acceleration = dv/dt = a while in circular motion angular acceleration = d𝛚/dt = 𝛂 whenever 𝛂 is positive its mean that angular velocity 𝛚 is increasing whenever 𝛂 is negative it mean that angular velocity 𝛚 decreasing when 𝛂 =0 its mean that 𝛚 is constant you can experience when fan is on then 𝛂 is positive and angular speed is increasing after sometime 𝛂 becomes zero then angular speed is constant when fan is off it is reverse of first case you can notice it is best example.

In linear motion at constant acceleration we have three motion equation  v = u+at, v² = u²+2as , s = ut+1/2at² similarly in circular motion we have equation 𝛚f = 𝛚i+𝛂t  , 𝛚²f = 𝛚²i+2𝛂𝜃, 𝜃 = 𝛚t+1/2𝛂t² you can use this formula to solve the numerical problem for circular motion questions we will continue in next post i hope you have enjoyed learning Physics circular motion equations thanks for reading.

Dated 3 Sep 2018.