What is Rotational motion: Definition and 609 Discussions
A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
Because it rotates around its axis, then it has a rotational kinetic energy. But when it orbits the Sun, then it has an another rotational energy too. Would it be ##E_\mathrm{rot} = \frac 12 (\frac 25 MR^2+ Md^2) {\omega}^2 ##, where ##d## is the distance between the Sun and the Earth. I...
[Mentor Note: See post #10 below for an updated problem statement using LaTeX and with a better drawing]
what i want is to find the axis of rotation when the centre of gravity and point on which external force is acting is given along with the magnitude and direction of force. In the example...
i,j,k arevector
I know L=P*r=m*v*r=m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k=mabωk.
but why m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k.I need some detail.
please help me.
I am using the following formula to solve this problem.
$$ L_a= L_c + \text { (angular momentum of a particle at C of mass M)}$$
Because the point C is at rest relative to point A, so the second term in RHS of above equation is zero. Hence, the angular momentum about A is same as angular...
I have come up with two different approaches, but I'm not sure which one is correct since they give different answers.
We use the following equation to get the total moment of inertia.
##I_o## = moment of inertia of disk about O axis + moment of inertia of road about O axis
Approach 1...
I think the the time given doesn't matter since no torque is acting on the system, but not sure. Therefore, all we need is to determine the angular momentum about the axis passing through O and perpendicular to the plane of disk. This will involve finding the moment of inertia of smaller disk...
I'm now learning about rotational motion without slipping and it's really hurting my brain to think about. Imagine a cylinder rotating on a flat plane.
I can accept that there is both translational and rotational motion. For example, a given point on the circumference of the cylinder follows a...
They say that a rotating knife thrown is more dangerous than a knife thrown straight
I find it weird
If the knife is rotating, it will experience more air drag than if thrown straight which will also depend on plane of rotation(For some reason, I don't know, it experiences more drag if...
I have a pencil of Iron of length ##L## rotating about its center in a plane at constant angular velocity ##\omega##. The tip of the pencil in Newtonian mechanics has linear velocity ##\frac{\omega L}{2}##. It can exceed ##c##, of course.
Now let us complicate this. Assume the center of the...
I know the answer is 170 but I am not sure how to get there. I tried doing things backwards
g=9.8
t = fr = mgr
0= 170 + tbl - tbr - 5x9.8x1.5
0= 170 + tbl - tbr - 73.5
-96.5 = tbl - tbr
-96.5 = 18*9.8 * 0.2 - 18*9.8*1.4
-96.5 does not equal -211.68
53 rpm equals 5.55 rad/sec
multiply 5.55 by 2pi to get angular velocity of 34.8717
Is the answer 34.8717?
What should I have done to more accurately solve the problem with a better understanding?
What other steps should I take when solving similar problems?
and lastly,
Is the mass relevant...
mball = 2 kg, mputty = 0.05 kg, L = 0.5 m, v = 3m/s
a) Moment of inertia : I = (2mball + mputty ). ¼ L^2 = 0.253125 kg.m^2
Linitial = Lfinal => mputty. v. r = I.ω => ω = (4.mputty.v.r) / I = 0.148 rad/s
b) K initial = 1/2 m v^2 = 0.225 J
K final = 1/2 Iω^2 = 2.85.10^(-3) J => Kfinal /...
The solution states that there's no rotational motion when ##C## is cut (the motion is curvilinear), so we can take torques with respect to the centre of mass of the plate. But, isn't it rotating? I think of it as a pendulum, which describes a circular motion. What's the difference? Wouldn't the...
I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
The question was:
I will also include the solution:
So, what is the justification of the first formula [ω=√(C/I)]? I know how to derive simple harmonic equations, this one as I guess is probably similar? But I cannot connect as to how C is used exactly.
And the second formula [ω'=ωβ], I...
Very confused at this.
https://courses.lumenlearning.com/physics/chapter/10-6-collisions-of-extended-bodies-in-two-dimensions/
"Consider the relatively simple collision shown in Figure 2, in which a disk strikes and adheres to an initially motionless stick nailed at one end to a frictionless...
Friction provides the necessary torque for rolling without slipping.So Rotational Energy must increase.Simultaneously acceleration of centre of mass down the inclined plane is positive so Translational energy also must increase.Overall The Gravitational Potential Energy is getting converted to...
If I take the three masses individually and try to calculate the moment of inertia of the system separately then
I=(m*0²)+(m*(l/2)²)+(m*l²)
=ml²/4 +ml²=(5/4)ml²
But If I try to calculate Moment of Inertia of the system using its Centre of mass then
As centre of mass is located at the the...
I'm not sure as to why my working is incorrect. When the sign on a_x is postive, i get t = \frac{R\omega_0}{3\mu_kg} which would give the correct value for distance if plugged into the kinematic equation. However, I'm not sure why a_x would be positive though since the friction force is pointing...
Hello, I'm stuck in this rotational motion problem (advanced high school level).
Source: Problems in General Physics- IE Irodov
My attempt(s):
First I tried using work done by the moment of friction (mgkR) and equated it with change in KE.
I got the answer as ## \frac{R (\omega_0)^2}{8 \pi...
I got a confusion about the sings in the angular acceleration. When dealing with system of pulleys, how to define where is the positive and negative direction of the motion and will the choose of positive direction of angular acceleration will effect the positive direction of linear acceleration
Hi folks! I was teaching myself rotational motion when encountered an example which states as follows:
My questions:
1. I do not understand why pulling the cord moves the rotating spool to the right. There were some discussions on stackexchange...
Hi there
I have been having a go at this question and I'm uncertain if my answer to part b) is valid?
The problem is when I plug this into the calculator I get 6.379... revs however this doesn't make sense to me. 2*pi is roughly 6.28 radians so doing 4.061... rads / 6.28 rads = 0.647 revs...
Here is the problem that I am finding difficult to answer
I had tried using conservation of energy to do this question
Where I know that the gravitational potential energy at the top of the slope equals to the sum of both the linear and rotational kinetic energy at the bottom of the slope...
I have the moment of inertia for the core(initial) and full body(final) but my answer for the moment of inertia for the arms(initial) was incorrect.
Arms(initial) moment of inertia:(1/12)(6)(1.7^2)=1.445 this is incorrect for some reason
Core(initial) moment of inertia: .9558
Full...
The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot...
Hi all,
I found this problem in a new textbook I'm working through.
And my energy conservation equation was ## mg\frac {h}{2} = \frac {1}{2} I ω^2 + mg \frac {h}{2}*sin(55) ##
My solution was wrong and after checking why I found that they used cos(35) as the angle. The rest was the same.
I'm a...
I have a solution, However Cant understand 1 point.Now, This is the solution:
##N_2 l cos\theta + \frac 1 2 F_g l cos\theta - f_2 l sin\theta = 0##
## N_2(1 - \mu tan\theta) + \frac 1 2 F_g = 0##
This is the the point that I don't like - yes it is less that 0, but it's even less that...
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...
First time poster here, thanks in advance!
I have a project I'm working on, and I'm looking for a way to limit the rotational motion of a shaft inside a cylinder. The cylinder is fixed, and the shaft is spinning inside the cylinder coaxially. Basically, torque will be applied to the shaft...
Homework Statement
"A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD...
Homework Statement
In the figure attached, what is the torque about the pendulum's suspension point produced by the weight of the bob, given that the mass is 40 cm to the right of the suspension point, measured horizontally, and m=0.50kg?
Homework Equations
tau = rFsin (theta)
or
tau = lF...
http://www.animations.physics.unsw.edu.au/jw/rotation.htm#rolling
I have set up an apparatus similar to what the above link says (the first bit about brass object with shaft). So basically, the shaft is in contact when the brass is first rolling, then it suddenly accelerates when the edge of...
Homework Statement :[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions.
1) The angular velocity of system...
Hello
Consider a pulley with a rope winded up around it, and two solids attached to the rope from each side. It is intuitive that the solid with the most mass will impose the direction of the rotational motion of the system ( note that the pulley can rotate), but i'd like to know how can we...
Homework Statement
A thin rod of length ' L' lies on the + x-axis with it's left-end at the origin. A string pulls on the rod with a force 'F' directed towards a point 'P' a distance 'h' above the rod.
Where along the rod should you attach the string to get the greatest Torque about the...
<< 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...
Homework Statement
A 10 g bullet traveling at 400 m/s strikes a 10 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door immediately after impact?
Homework Equations
p[/B]= mv
L = Iω...
Homework Statement
If I have an object with mass M. Place it on a spinning disk at radius R and the coefficient of friction is μ what is the maximum velocity I can spin the disk without the object slipping? I have the actual values for the problem, but I'm much more interested in how to get...
Homework Statement
The following question involves a torque acting on a particle in rotational motion. It provides practice with the various equations for angular velocity, torque etc A particle of mass ##m## initially has position...
Homework Statement
An airplane propeller is 2.78 m in length (from tip to tip) and has a mass of 127 kg . When the airplane's engine is first started, it applies a constant torque of 1880 N⋅m to the propeller, which starts from rest.
Part D
What is the average power output of the engine...
Homework Statement
Given an plate that has 2 pins attached to it. Each pin has a single balanced circular disc firmly attached to it. Each pin can rotate on their axis in both clockwise and anti clockwise direction. (See image below)
Now, assume the discs are rotating with the same angular...
As a spinning mass is unwound, angular momentum is conserved, meaning ##Iω## remains constant. However, since rotational energy is proportional to the square of the angular velocity, how is it possible for energy to be conserved as well?
Homework Statement
A uniform, spherical cloud of interstellar gas has mass 2.03×1030 kg and radius 1.03x1013m and is rotating with period 1.43×106 years. The cloud collapses to from a star 7.03x108m in radius. Find the star's rotation period.
Homework Equations
I1ω1=I2ω2
Θ=ωt
The Attempt at a...
Suppose there are two discs held in contact such that they rotate around the same axis of rotation. A torque is applied to one of the discs, and due to friction the other disc accelerates. Using calculus I found the torque applied due to friction for a disc to be ##\frac {2μF_N r} {3}##, meaning...
Homework Statement
[/B]
A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...
Homework Statement
There are two discs with equivalent density and thickness. One has radius r1 while the other has radius r2. r2 is twice as great as r1 The larger disc has an initial angular velocity ω. The two discs then come in contact with one another and friction causes them to rotate...
Homework Statement
[/B]
A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2)
Homework Equations
[/B]
Find the speed of the wheel when it is 10m below the top.
The Attempt at a Solution
[/B]
mgh = 1/2mv^2 + 1/2IW^2
W=...