From this equation we see that the acceleration vector has magnitude
$A{\omega}^{2}$ and is directed opposite the position vector, toward the origin, because
$\overrightarrow{a}(t)=\text{\u2212}{\omega}^{2}\overrightarrow{r}(t).$
Circular motion of a proton
A proton has speed
$5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{m/s}$ and is moving in a circle in the
xy plane of radius
r = 0.175 m. What is its position in the
xy plane at time
$t=2.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-7}}\phantom{\rule{0.2em}{0ex}}\text{s}=200\phantom{\rule{0.2em}{0ex}}\text{ns?}$ At
t = 0, the position of the proton is
$0.175\phantom{\rule{0.2em}{0ex}}\text{m}\widehat{i}$ and it circles counterclockwise. Sketch the trajectory.
Solution
From the given data, the proton has period and angular frequency:
The position of the particle at
$t=2.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-7}}\phantom{\rule{0.2em}{0ex}}\text{s}$ with
A = 0.175 m is
From this result we see that the proton is located slightly below the
x -axis. This is shown in
[link] .
Significance
We picked the initial position of the particle to be on the
x- axis. This was completely arbitrary. If a different starting position were given, we would have a different final position at
t = 200 ns.
Circular motion does not have to be at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of the motion.
In uniform circular motion, the particle executing circular motion has a constant speed and the circle is at a fixed radius. If the speed of the particle is changing as well, then we introduce an additional acceleration in the direction tangential to the circle. Such accelerations occur at a point on a top that is changing its spin rate, or any accelerating rotor. In
Displacement and Velocity Vectors we showed that centripetal acceleration is the time rate of change of the direction of the velocity vector. If the speed of the particle is changing, then it has a
tangential acceleration that is the time rate of change of the magnitude of the velocity:
The direction of tangential acceleration is tangent to the circle whereas the direction of centripetal acceleration is radially inward toward the center of the circle. Thus, a particle in circular motion with a tangential acceleration has a
total acceleration that is the vector sum of the centripetal and tangential accelerations:
The acceleration vectors are shown in
[link] . Note that the two acceleration vectors
${\overrightarrow{a}}_{\text{C}}$ and
${\overrightarrow{a}}_{\text{T}}$ are perpendicular to each other, with
${\overrightarrow{a}}_{\text{C}}$ in the radial direction and
${\overrightarrow{a}}_{\text{T}}$ in the tangential direction. The total acceleration
$\overrightarrow{a}$ points at an angle between
${\overrightarrow{a}}_{\text{C}}$ and
${\overrightarrow{a}}_{\text{T}}.$
Questions & Answers
A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK
What is Newtonian mechanics in physics?
Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
Bhaskar
tq u.
Prema
these are the best physics books one can fond both theory and applications.
Bhaskar
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here...
.
1. Newton's laws of Motion, are they applicable to motions of all speeds?
2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
Manash
The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
It states that, " If two vectors are represented in magnitude and direction by the two sides of a triangle, then their resultant is represented in magnitude and direction by the third side of the triangl " .