In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same.
Examples of circular motion include: an artificial satellite orbiting the Earth at a constant height, a ceiling fan's blades rotating around a hub, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.
Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation. Without this acceleration, the object would move in a straight line, according to Newton's laws of motion.
My solution was as follows:
$$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$
The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...
So first I found the velocity of the ball at the bottom of the swing from the force equations, which I got to be 4.9 m/s and this is only in the x-direction. Then using the projectile motion for delta y I found time, which is 0.2s. Then using that time I found the delta x to be 0.98m.
I just...
Hello ,
First of all , I am still new to circular motion or any motions in general and still relatively learning so please bear with me.
1 . The direction of the tangential acceleration is parallel to the net velocity and that of radial of perpendicular to the velocity. So the direction of net...
My work so far is pretty basic, but I'm not too sure how to continue off from here. I haven't included the 2 dimensional aspect of it either, but I would presume that the rate of decrease in length is more sped up in that case? Would appreciate any help :(
(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing)
I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...
As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then...
I would really appreciate some help with this problem regarding non-uniform circular motion, in which a body is accelerating as it follows a circular path.
If we take Example 1, a body starts at Point A with an angular speed of 180°/s. The body accelerates to Point B and reaches it some time...
This question is very confusing since I don't see two distinct particles that are exerting a gravitational force on each other. Also to complicate matters, a gas is made of many individual particles and I don't know how to determine the gravitational force on a single particle from so many other...
Hello,
Apologies if this is in the wrong section, it's related to circles so I figured Geometry was the best place. I found a very good example online that explains how to determine a future position of an object undergoing uniform circular motion:
(Note that they made a mistake by writing...
##ω = \frac {k} {\sqrt{φ}}##
What is the angle between acceleration and velocity after 1spin (2π radians)?
First I decided to find out what is the angular acceleration:
##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = -...
a.)N cos θ=mg
N sin θ=mrw^2 sin θ
cos θ=g/rw^2
b.) My question is reaction force =N ? or =F=mg tanθ ?
If it is N then N=mg cosθ =mg^2/r w^2 or N=mg/cosθ =mrw^2 ?
Thank you
My solutions (attempts) :
a> w=v/r | r=6.35x10^6m | therefore V=7.04x10^-5 m/s
b> speed of rotation is faster at the equator than the pole as w=v/r. As w remains constant, as r increases towards the pole V has to decrease.
c> F = W - R
d> Stuck here. I presume that I have to use the equation...
Below is my working out. If you could have a look at my answers and see if they are correct and then advice me on how to improve my solutions for Parts I and II, and how to answer F and G with the given information. Thanks in advance!
Parts aand b are diagrams so please refer to the attached...
Why I think gravity *is* the only force doing work on the rider:
1) The only forces acting on the rider are gravity and the normal force. Broken down into their component vectors, we have:
-> The component of the force of gravity moving parallel to the rider's direction of motion
-> The normal...
Situation: Let’s say we have a wire bent into a circular shape, there lies a bead through the wire and it can slide through it. The wire is kept in vertical plane and is swung along the axis AB.
My question : How the centripetal force is provided to the bead?
The bead will go into a...
Diagram for question 1:
I know the mass, I need Fg.
My work:
Main equation: g = Fg/m I need to find Fg.
Fg= Fc - Fn [Fn = 21 N Fc = ?] {I need to find Fc.}
Fc = ma --> Fc = (mV^2)/ r [Mass = 1.3kg V = ? r = 0.70] {Now I need the velocity at that point where Fn = 21 N (the top of the...
Centripetal force is defined as the force causing the body to follow a curved path, acting towards the center and always orthogonal to the direction of motion. For uniform circular motion the formula for centripetal acceleration is $$a_c = \frac{v^2}{r}$$.
But my understanding of centripetal...
I think I have solved the first three, and only really need help on question four.
For number one, I used Fc = (Mv^2)/R and just rearranged it for velocity so I ended up with v = sqrt(ac * R)
For number 2 I used Ff = Fn*mu and got Mg*mu = Ff
For number 3 I used w = Ff*d and got w = -Mg*mu*l...
1. For the car to apply brakes, we have ##v^2=2ar⇒a=\frac{v^2}{2r}=μg\;\;[ma=μmg]⇒v=\sqrt{2μgr} ##
2. For the car to go in a circle ##\frac{mv^2}{r}=μmg\Rightarrow v=\sqrt{\mu gr}##.
We find from above that the maximum velocity ##v## possible to avoid a collision is ##\sqrt{2}## times as much...
I wrote Newton's equations for each body (I took ##x## as the axis aligned with the tension)
##m_1##:
##x)f*_1 -T_1+T_2=0##
Where ##f*_1=\omega ^2 r_1##
##m_2##
##x)f*_2 -T_2=0##
##x)f*_2=T_2##
Where ##f*_2=\omega ^2 r_2##
I wrote that ##T_2=1100 N## and solved for ##\omega##, and I got...
1). I calculated maximum safe velocity using the equation -
V(max)=√200x10x0.2
=20m/s
So the speed at which car is traveling is greater than the safe speed.. So the car should skid. So why 4th option is not correct ?
The solution to the problem simply states: "Use of mv^2/r = 2000. T = (2000 + 7500) = 9500N". I don't understand this solution. Nothing more is provided. I don't know how you are supposed to find the radius (in order to use the centripetal force formula) merely from the information provided...
Homework Statement
A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...
Homework Statement
A cylinder rolls without slippage on a horizontal plane. The radius of the cylinder is equal to r. Find the radious of curvature of the trajectory of points A and B.
Homework Equations
Ciruclar motion equations.
##R=\frac{1}{C}##
The Attempt at a Solution
First I drew...
Homework Statement
A particle A moves along a circle of radius ##R = 50 cm## so that its radius vector ##r## relative to the point O (Fig. 1.5) rotates with the constant angular velocity ω = 0.40 . Find the modulus of the velocity of the particle, and the modulus and direction of its total...
a disc or radius r = 16cm starts spinning from rest with a uniform angular acceleration of 8.0 rad/s^2. at what time is its tangential acceleration twice the centripetal acceleration.
i figured out the tangential acceleration is:
Atan = α/R = 8 / .16 = 50 m/s^2
and the centripetal...
A constant tangential force of magnitude 12N is applied to the rim of a stationary, uniform circular flywheel of mass 100kg and radius 0.5m. Find the speed at which the flywheel is rotating after it has completed 25 revolutions?
I know that this can be done using work-energy. But since a...
Homework Statement
Homework Equations
L = T-V
For constant frequency tangential velocity is (radius)*(w)
The Attempt at a Solution
I need to find r(t) using the Langrangian L = T-V
I just was not sure whether I am on the right track for calculating the total kinetic energy for the above...
I' m trying to derive the work done by a torque from W = ∫ F ⋅ ds and I' ve looked up the internet, it said:
W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 )
it can be written as
W = ∫ F ⋅ dθ x r
this is a vector triple product , thus can also...
Homework Statement
An object moves at constant speed in a circular path. True statements about the motion include which of the following?
a) the velocity is constant
b) the acceleration is constant
c) the net force on the obj is 0 since its speed is constant
Homework Equations
hm none...
Homework Statement :[/B]
One swings a rock at the end of a string. We wish for the string to remain taut and for the rock to travel in a circulat path, in a vertical plane. What mathematical condition must the centripetal acceleration of the rock satisfy for the string to remain taut when the...
Homework Statement
A ball on the end of a string is whirled around in a horizontal circle of radius 0.250m. The plane of the circle is 1.06m above the ground. The string breaks and the ball lands 1.90m (horizontally) away from the point on the ground directly beneath the ball's location when...
Homework Statement
A particle is moving parallel to x-axis in the positive direction with velocity v such that at all the instants the y -axis component of its position vector is constant and is equal to 'b'. Find angular velocity about origin.
Homework Equations
The Attempt at a Solution
I...
What If the velocity of particle moving in a circular orbit has increased , would the particle be no longer in circular orbit or it would go in an orbit with bigger radius?
I've been given a question to find the magnetic flux density of the Earth if an electron is orbiting near to the surface. The answer to the question makes the magnetic force equal to the centripetal force and solves for B from there.
However, I am confused to why the gravitational force has no...
Homework Statement
Why do the left wheels of a car rise when it takes a sharp left turn (that is it lurches towards the right)?
Homework Equations
$$a_c= V^2/R$$
The Attempt at a Solution
I started by imagining the car as being a part of a very large ring, dx.
Since it's taking a left turn...
Homework Statement
This question is referring to the classic ball in a loop question where it is dropped from a height and slides into a loop de loop.
Derive an expression in terms of theta the velocity of the ball at the time it loses contact with the track. Theta is measured from the...
I understand that the centripetal force on an object of mass 'm' is (mv2)/r
However, isn't this for an object going around in a circle? Suppose I have a curve (0.0033x2+−1.0038x+98.2331). What would be the fastest speed around this curve on the bounds x ->
Please note that we would...
Homework Statement
The Russian Mir space station had a mass of 130 tonnes and orbited Earth at an altitude of 480km with an orbital speed of 7621.4m/s. The diameter of Earth is 12 760 km.
a) What centripetal force was acting on it?
b) Find the value of the acceleration due to...
<< Mentor Note -- Two threads on the same subject have been merged >>
I am a junior enrolled in IB Physics at the standard level at my high school. As a part of the curriculum we must perform an Internal Assessment (IA) which involves performing an experiment and performing calculations and it...
In circular motions, one can measure the NetForce on an object with this formula:
ΣF = m*v^2/r.
But is this formula valid even if the orbital speed of the object is constantly increasing (or constantly decreasing)?
A mass m = 0.15 kg is attached to a massless string and rotates at constant speed v = 4 m/s in a horizontal circle of radius 2 m. The tension T (in N) in the string is: (a) 1.1 (b) 1.9 (c) 2.4 (d) 3.3 (e) 4.9
I would assume that first I calculate the centripetal acceleration by using v^2/r =...
Homework Statement
Gravity causes a centripetal force that allows satellites to travel around planets.
How fast must a 102-kg satellite travel to maintain a circular orbit 352 km above Earth's surface?
Homework Equations
F=m(v^2/r) -----> (F/m) x r= v^2, then square root
F= force
m=mass...
Hi!
I am currently working on a project that includes rotating a water-filled container. The container is NOT spinning about its vertical axis, but about the vertical axis of the rotating disc.
I am aware that the surface shape of water in a rotating bucket takes the shape of a parabola when it...
In circular motion
1) V = rw and ##\vec V## = r ω##\vec e_{tan}##
2) a = rα and ##\vec a## = -##\frac{v^2}{r}####\vec e_{rad}## + rα##\vec e_{tan}##
Where ##\vec e_{tan}## is the unit vector along the tangent in increasing direction of θ
And ##\vec e_{rad}## is the unit vector along the radial...
Homework Statement
An experiment that involved swinging a mass in a circle was conducted. After graphing both sets of data, I obtained linear graphs of which I calculated the slopes for. I got a slope of 3.5 for the force vs frequency^2 graph and a slope of 0.73 for the radius vs period^2...
Homework Statement
A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center...