Rotational kinematics Definition and 19 Discussions
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degrees of freedom.
An example where rotation representation is used is in computer vision, where an automated observer needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate system). The basic problem is to specify the orientation of these three unit vectors, and hence the rigid body, with respect to the observer's coordinate system, regarded as a reference placement in space.
In the solution, the term Lcm and Icm is used. Explain the meaning of these terms? I think cm stands for centre of mass. why that is used in the subscript?does the term angular momentum from the centre of mass of the sphere makes sense? Is the term Lcm and Icm stand for angular momentum of the...
My line of thinking is as follows:
\omega_{PQ} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2}
Similarly for rod ##QR##
\omega_{QR} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2}
Is my reasoning correct?
I apologize in advance for any errors in my concepts or assumptions. Feel free to correct me wherever I am wrong. Thanks in advance for the help.
There is a vertical shaft which will be operated at around 600 rpm (N) which can be achieved in 2 seconds (or even 4 just an assumption). The shaft...
I was first wondering wether we can solve this question by applying conservation or energy or not but after googling it I found that we can't apply conservation of energy since there will be some energy lost in this case. I don't know how this energy is getting lost.
My second doubt was if we...
First we let the static friction coefficient of a solid cylinder (rigid) be ##\mu_s## (large) and the cylinder roll down the incline (rigid) without slipping as shown below, where f is the friction force:
In this case, ##mg\sin(\theta)## is less than ##F_{max}##, where ##F_{CM,max}## is the...
Hello,
Here in this thread I will derive formulas for relation between two wheels, either teethed (e.g. gears) or non-teethed.
In wheel relationship, we have three cases:
Two wheels at the same axle
Two wheels intersected in parallel (meshed)
Two wheels connected by a belt
We will examine...
torque=Force*radius*sin(theta)
center of mass x direction = ( 0(6 x 10^9 kg)+ (118m)(6 x 10^9 kg)+ (236m)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 118m
center of mass y direction = ( 0(6 x 10^9 kg)+ (140m)(6 x 10^9 kg)+ (0)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 46.7 m
radius = (118^2 + 46.7^2)^(1/2) =...
moment of inertia = (1/3) (2.1kg) (1.2m)^2 = 1.0 kgm^2
center of mass= (0.6i, 0j)
magnitude of the gravitational torque=9.8m/s^2*2.1kg*0.6m= 12.34N*m
position of the new center of mass now :
x direction = cos(20)*0.6m=0.56m
y direction= -sin(20) * 0.6m = -0.2m
change in gravitational...
Homework Statement
A boomerang is thrown with an initial linear velocity of 5 m/s at an angle of 30 degrees vertically. The initial angular velocity is ##2\frac{revolutions}{s}## At its peak, it has a displacement about the z axis of 2 meters and about the x-axis of 10 meters. The force applied...
Homework Statement
You buy a bottle of water in the store and place it on the conveyor belt with the longitudinal axis perpendicular to the direction of movement of the belt. Initially, both the belt and the bottle are at rest. We can approach the bottle as one cylinder with radius ##R##, mass...
Homework Statement
.A cylinder P of radius rP is being rotated at a constant angular velocity ωP along positive y-axis with the help of a motor about its axis that is fixed. Another cylinder Q of radius rQ free to rotate about its axis that is also fixed is touched with and pressed on P making...
Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule.
According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction...
Homework Statement
A uniform cylinder of mass ##M## and radius ##R## is released from rest on a rough inclined surface of inclined surface of inclination ##\theta## with the horizontal as shown in the figure. As the cylinder rolls down the inclined surface, what is the maximum elongation in...
Homework Statement
I am referring to this thread and question: https://www.physicsforums.com/threads/rotation-of-a-spool-about-rough-ground.295666/
Here is the problem, restated:
Homework Equations
##\tau_{net} = I\alpha##
##\tau = Frsin(\theta)##
##F_{net} = Ma_{cm}##
##\alpha = a_{cm} /...
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Thread
forces
mechanics
moment of inertia
rotation
rotationalkinematics
Homework Statement
A small pine tree has a mass of 15kg. Its center of mass is located at .72m from the ground. Its trunk is sawed through at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 17° angle with the...
[Note: Post moved to homework forum by mentor]
So I stumbled upon a reviewer for my physics exam tomorrow and I was wondering how the equation was formulated. Your help is very much appreciated :) ! Normally I would consult my professor for this but it's Sunday in my country today so I can't...
A very small coin is at distance 10.5 cm from the spindle of a turntable. The turntable starts spinning from rest with constant angular acceleration. In 0.133 s the coin's centripetal acceleration is 1.39 times its tangential acceleration.
1)Find the turntable's angular acceleration.
2)Find the...
Homework Statement
A girl and a boy are sitting in a see saw. The girl is 36 kg and sitting 5 m from the fulcrum. The boy is sitting 3 m from the fulcrum. Calculate the mass of the boy and the force on the fulcrum.
Homework Equations
Fr1=Fr2
The Attempt at a Solution
I solved for the boys...
Homework Statement
A wheel of radius R starts from rest and accelerates with a constant angular acceleration α about a fixed axis. At what time t will the centripetal and tangential acceleration of a point on the rim have the same magnitude?
Homework Equations
acp=r x ω2
at= r x α
ω= 2π / T...