# Kinematics: Analyzing circular motion of a particle

• Edward Hillsby
In summary, you know ##v = u + at## and you know ##v.\ \ ## What can be easier ?SUVAT: v=u+at, r= r0+u0t+1/2 a t^2UK is using inches and still has some catching up to do :-pSo: you know ##v = u + at## and you know ##v.\ \ ## What can be easier ?Tip: Make a plot !You can make a plot by using the plot function in R.
Edward Hillsby
Homework Statement
A particle moves with constant acceleration and its velocity at time t :

v= (5-0.1t)i +(3+0.2t)j

1. find a, u

2. find the time t when particle is travelling in direction NE and find its speed.

3. find the distance and bearing of the particle from the starting point at that time.
Relevant Equations
SUVAT, TRIG, Bearing

Hello @Edward Hillsby, !

Apparently you know about SUVAT. Which ones in particular can be used here ?

Edward Hillsby said:
Sure! However, there are some requirements to get help at PF. Read here what is u anyway ?  ah ! ##v_0## !

Tip: Make a plot !

u/initial velocity =v0, u is popular and very common in UK

SUVAT: v=u+at, r= r0+u0t+1/2 a t^2

UK is using inches and still has some catching up to do

So: you know ##v = u + at## and you know ##v.\ \ ## What can be easier ?
BvU said:
Tip: Make a plot !

I am not sure how to use trig for the NE direction. It is 45 degree or pi/4, slope= 1

Tip: Make a plot ! All will be revealed !

berkeman
is it vy sin 45=uy+ayt?, it does not work. What plot?

Edward Hillsby said:
is it vy sin 45=uy+ayt?, it does not work
No. ##v_y = u_y + a_y t\ \ ## and ##\ v_x = u_x + a_x t ##

I am beginnning to fear you overlook the vector character of ##\vec r, \ \vec v,\ \vec a ## ?

Edward Hillsby said:
What plot?
v= (5-0.1t)i +(3+0.2t)j ##\ \ ## You know what the ##\ \hat\imath\ ## and ## \ \hat\jmath\ ## stand for ?
Plot ##v_y(t)## as a function of ##v_x(t)## for ##t=0, 1, ...15## sMay I also advise you to use super- and subscripts ?

It is working. Thanks, guys from yahoo and overflow struggle to answer. I did not overlook vectors, but was to obsessed with trigs. 1 smart mathematician got similar result, using trigs: tangent, arcus tangent and got assumption pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right? I do not know what is different between ry and r_y. Thanks

Edward Hillsby said:
It is working.
Without the plot ?

Edward Hillsby said:
1 smart mathematician got similar result
For what ?
Edward Hillsby said:
pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right?
I don'know if it's right. But intellegible it sure isn't

so, can angle in certain condition, here slope =1, be expressed by opposite/adjacent in right angle triangle? It mean angle = tangent??

Edward Hillsby said:
so, can angle in certain condition, here slope =1, be expressed by opposite/adjacent in right angle triangle? It mean angle = tangent??
The slope is the tangent of the angle. An angle π/4 gives a slope of 1. tan(π/4)=1.
Edward Hillsby said:
pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right?
I assume you are using rx, ry for coordinates of position.
ry=(π/4)rx would mean the position is a bit E of NE from the origin (ry<rx), so it is wrong on two counts:
1. For exactly NE you would want the coordinates equal. I.e. (ry/rx)=1=tan(π/4).
2. The condition you should be applying is that the velocity is NE.

Last edited:
thanks

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path, where the distance from the center point remains constant. This type of motion can be seen in objects such as a Ferris wheel or a spinning top.

## 2. How is circular motion different from linear motion?

Circular motion involves an object moving along a curved path, while linear motion involves an object moving along a straight path. In circular motion, the direction of the object is constantly changing, while in linear motion, the direction remains constant.

## 3. What is the difference between angular velocity and linear velocity?

Angular velocity is the rate at which an object rotates or moves around a central point, while linear velocity is the rate at which an object moves along a straight path. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

## 4. How do you calculate centripetal acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path. It can be calculated using the formula a = v^2/r, where v is the velocity of the object and r is the radius of the circular path.

## 5. What is the relationship between centripetal force and centripetal acceleration?

Centripetal force is the force that keeps an object moving in a circular path. It is directly proportional to the centripetal acceleration, meaning that as the centripetal acceleration increases, so does the centripetal force. This relationship is described by the equation F = ma, where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration.

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