What is Rotational kinematics: Definition and 131 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...
A potter's wheel with a 35.9 cm radius rotates with a 2.91 rad/s2 angular acceleration. After 5.37 s, the wheel has rotated through an angle of 77.7 rad.
a)What linear distance did a point on the outer edge travel during the 5.37 s?
b)What was the initial angular velocity of the wheel?
c)What...
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 disk is initially at rest. A penny is placed on it at a distance of 1.4 m from the rotation axis. At time t=0s, the disk begins to rotate with a constant angular acceleration of 1.9 rad/s^2 around a fixed, vertical axis through it's center and perpendicular to it's plane...
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} /...
Homework Statement
A wheel rotates with a constant angular acceleration of π rad/s^2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is its angular velocity at the beginning of the time interval?
Homework...
Homework Statement
A small spherical rock of mass collides in space with a large spherical rock of mass as indicated in the diagram. After the collision the rocks stick together to form a single spherical object.
https://postimg.org/image/fltmg3bj5/
(New here so I've no clue how to upload...
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...
Homework Statement
In a playground there is a small merry-go-round of radius 1.20 m and mass 220 kg. The radius of gyration is 91.0 cm. A child of mass 44.0 kg runs at a speed of 3.00 m/s tangent to the rim of the merry-go-round when it is at rest and then jumps on. Neglect friction between the...
Homework Statement
A wheel of diameter 45.0 cm starts from rest and rotates with a constant angular acceleration of 2.50 rad/s2 . At the instant the wheel has completed its second revolution, compute the radial acceleration of a point on the rim in two ways.
1 Using the relationship...
[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...
Here is the problem I am working on. I have found answers for all of them except part (f), which is the one I need help with. I will report the answers I have so far:
A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00...
Homework Statement
A computer disk drive is turned on starting from rest and has constant angular acceleration.
If it took 0.680s for the drive to make its second complete revolution, how long did it take to make the first complete revolution? (t=?)
Homework Equations
Θ=(ct^2)/2 (i think)
The...
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...
Homework Statement
A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of
6.55 kg, a radius of R = 38.0 cm and is in the shape of a ring. A mass M = 1.85 kg is attached to
the end of a string which is wrapped around an inner hub which has a radius r = 5.40...
Homework Statement
This isn't so much of a problem as a general question. I am trying to find the starting velocity of a spinning ball going upwards (in air, close to Earth's surface, only force acting on it is the gravitational force) until its linear velocity reaches zero. I found the initial...
Good afternoon! I've been mulling over this question for a bit and I can't seem to understand what it is asking. This is a question for an introductory calculus-based physics university course.
1. The Problem:
A uniform disk, such as a record turntable, turns 8.0 rev/s around a frictionless...
Homework Statement
A phonograph turntable with an initial angular velocity of 78 rpm continues turning for 40 rotations after being switched off. What is the angular deceleration of the turntable? Assume constant angular deceleration.
Homework Equations
\alpha=(\omega-\omega0)/t...
Homework Statement
A turntable is a uniform disc of mass m and radius R. The turntable is initially spinning clockwise when looked down on from above at a constant frequency f_0. The motor is turned off at t=0 and the turntable slows to a stop in time t with constant angular deceleration...
Homework Statement
Consider a system of two masses joined by a massless string with the string passing over a massless frictionless pulley with a radius of
5.0 cm.
The mass of the left is
9.00 kg
and the mass on the right is
1.60 kg.
Find the angular acceleration of the pulley when the...
1. Problem statement
2. Related equations
I = bmr^2
Energy equations (linear and rotational)
3. Attempt
Part a)
I know that the distance or height traveled by the box is [h - d] because center of the mass of box is just d. Initial kinetic energy of the box and cylinder is 0 and if only...
I'm trying to learn some physics on my own, using the internet as my main source of information.
Now, I'm a bit confused about some terminology, and I can't find anything about it...
Distance vs displacement in rotational kinematics!
Is there a similar difference as in linear kinematics...
Homework Statement
A barrel is lowered into a boat using the illustrated apparatus. The barrel can be considered to be a uniform cylinder with M=100kg and r=0.40m. The weight on the other end of the rope has m=30kg. Assume that the barrel does not slip against the wall, that the other 2...
Homework Statement
Determine the relationship between the angular
acceleration of the flywheel, the downward acceleration of the block, and the radius of
the ring.
Known data:
Mass Ring: 1.420 kg
Radius Ring (Inside, then Outside): 5.10 cm, 6.325 cm
Mass Disk: 1.455 kg
Radius Disk...
A flywheel 1.2 m in diameter is uniformly accelerated from rest and revolves completely 68 times in reaching a speed of 125 rev/min. Find the time taken to reach this speed
i have been given the correct answer as 65.29 seconds
Wht i have up to now
ω1 = 0
ω2 = 125 r/min = 125/60 =...
[b]1.
Consider a fan that has rotated by a total of 2 complete revolutions from where it started. This quantity (2 revolutions) is analogous to what quantity in linear kinematics?
Position
Displacement
Velocity
Speed
Time
Time
Homework Equations
I am...
Homework Statement
Each of the questions are either increase, decrease, equal, or undetermined.
1) You are sitting on a rotating chair, holding a 2 kg mass in each arm outstretched. When the masses are dropped, your angular momentum -------.
2) You sit in a rotating chair holding 2 kg...
1. A uniform rigid rod of length L and mass M is attached to a frictionless pivot point at one end. The rod is initially held completely horizontal and is released from rest. What is the linear and angular velocities at the instant the rod is in the vertical position?2. -ΔU = ΔK
3. -ΔU =...
Homework Statement
An electric turntable 0.710 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.230 rev/s. The angular acceleration is 0.887 rev/s^2.
A. Compute the angular velocity after a time of 0.192 s.
B. Through how many revolutions has the blade...
Homework Statement
A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 9.0 rev/s. In addition, the ball is thrown with a linear speed of 21 m/s at an...
Homework Statement
A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.40 rad/s^2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -24.0...
Homework Statement
A block with mass m is revolving with linear speed v1 in a circle of radius r1 on a frictionless horizontal surface (see the figure ). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r2.
Calculate the...
Homework Statement
A 45.0-cm diameter wheel, consisting of a rim and six spokes, is constructed from a thin rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 52.0m high.
a.) How fast is it rolling when it reaches the...
Homework Statement
Summary:
The pulley in the figure has radius (R) and a moment of inertia (I). The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is \muk. The system is released from...
Homework Statement
A thin uniform rod of mass (M) and length (L) is bent at its center so that the two segments are now perpendicular to each other.
a. Find its moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet...
The moon has a diameter of 3.48 x 10^6 m and is a distance of 3.85 x 10^8m from the earth. The sun has a diameter of 1.39 x 10^9 m and is 1.50 x 10^11 m from the earth.
(a.) What are the angles (in radians) subtended by the moon and the sun, as measured by a person standing on the earth...