What is Angular speed: Definition and 278 Discussions
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function.
Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.One revolution is equal to 2π radians, hence
ω is the angular frequency or angular speed (measured in radians per second),
T is the period (measured in seconds),
f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν).
wfinal=98.0 rad/s, dt=3.00s
w=(37 revs/3)=>w=(37 revs*(2*pi/1))/3=>w=77.493
a=(98-77.493)/3=>a=6.8357
My answer is exactly half of the correct answer. Where did I go wrong?
1) Applying conservation of linear momentum:
$$m.u = M.V + m.v$$
where ##V## is final linear speed of the rod
$$V=\frac{m.u-m.v}{M}$$2) Applying formula of circular motion:
$$V=\omega . r$$
$$\omega = \frac{\left(\frac{mu-mv}{M} \right)}{\frac{1}{2}L-x}$$
Is this correct?And can this be...
So clearly the easiest way to relate the angular speed to the linear speed would be to start from ##\tan(θ) = x/h## and take a time derivative of both sides. However, it also shouldn't be difficult to find the angular speed geometrically. Using the diagram below one can see that:
##sin(dθ) =...
I have seen the solution and understand it. The solution defines θ to be the angle between the falling rod and the table. It then equates initial PE to the final (PE+KE) where the final PE=0 and the final KE to be (1/2) Iω2+ (1/2) ma2ω2 to finally obtain ω = √(3g/2a)
But i would like to know...
and this is my solution
for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$
but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large
Besides, I don't know other Physics prevents...
The centre of mass of the rod would be at the middle of the rod i.e. at
l/2=[50*10^(-2)]/2
The force responsible for torque will be acting downwards = mg
The Torque = mg*l/2*sin(30) =mg*l/4
We know that Torque=I*alpha
Hence alpha = mg*l/(4*I)
Moment of inertia of rod about the end= ml^2/12 +...
initial total KE= (1/2)(0.6kg)(8m/s)^2 = 19.2J
(0.6kg)(8m/s) = (0.6kg+1.8kg)(vf)
vf= 2m/s
final KE= (1/2)(0.6kg+1.8kg)(2m/s)^2 = 4.8J
I tried to use linear speed=angular speed * radius : thus
2m/s= angular speed * (3.3m/2)
angular speed= 1.2 rad/s
Apparently that is wrong.
ω(10)=(1.3)∗(1.0−e^(−10/22) )= 0.475 rad/s
0.475 rad/s=0 +α(10second)
α=0.0475 rad/s^2
∫ω(t)=Θ =1.3t + 28.6e^(-t/22) | (t=10s, t=0)
total angle by which the wheel rotates over this period of t=10 seconds = 2.55 rad
Θ= 2(pi)(8m)= 1.3t + 28.6e^(-t/22)
0=1.3t + 28.6e^(-t/22) - 2(pi)(8m)
t=34...
Hello to all good people of physics forums. I just wanted to ask, whether the angular and linear (orbital) speed in perihelion of eliptical orbit are related the same way as in circular orbit (v = rw). If we take a look at the angular momentum (in polar coordinates) of reduced body moving in...
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...
Hello there, I'm new here and i need some help on my home work.
A DVD drive rotates at an angular frequency of 4800 rpm. a) what is it's angular speed in rpm? b) at 4800 rpm, what is the linear speed (in knm/hr) of (i) the center point and points (ii) 5 cm and (iii) 6 cm from the center?
Thanks!
How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)?
I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) ...
Homework Statement
A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30 degrees with the horizontal...
Homework Statement
A plank of wood sits on top of two rollers with radius of 44.4 cm. The plank is pulled forward so it moves at a constant acceleration of 2.24 m/s^2, starting from rest, and the rollers roll without slipping along the ground and in contact with the plank. What is the...
Homework Statement
A disk [m=0.1 Kg; R=0.1 m] rotates about its center of mass [w=40 rad/s], on a smooth floor. A bar [m=0.1 Kg; lenght=R=0.1 m] moves on the floor with a speed Vb=4 m/s. At one point, the bar hits disk's edge in an inelastic collision, and they start rotating together.
A)[Fixed...
Homework Statement
If we have a hollow ball completely filled with water which is rolling without slipping on a horizontal ground. If the water freezes which of the parameter will remain unchanged-
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Homework...
The two pulleys connected by a belt have a radii of 15 cm and 8 cm. The larger pulley rotates 24 times in 36 seconds.
a. Find the angular velocity of the small pulley in radians per second.
b. Find the linear velocity of a point on the belt that connects the two pulleys in centimeters per second.
Homework Statement
African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a
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Homework Statement
A floral clock in Japan has a radius of 15.5 m. If you ride a bike around the clock, making 16.0
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Homework Equations
ω = velocity/radius ; 1 rev=2*pi rad
The Attempt at a Solution
(16 rev*2*pi rad)/270 secs = 0.372...
A torsional pendulum made by suspending a horizontal uniform metal disk by a wire from its center. If the disk is rotated and then released, it willexecute simple (angular) harmonic motion. Suppose at t seconds the angular displacement of \theta radians from the initial position is given by the...
Let r = radius
See picture.
If r = 6 cm, R = 10 cm, and the angular speed of the larger wheel is 100 rpm, determine the angular speed of the smaller wheel in radians per minute.
Again, 1 revolution = 2 pi radians.
I need to use w = θ/t.
So, θ = 100 rpm • 2 pi radians.
θ = 200 pi...
I decided to change the radius.
Let r = radius
If r = 10 cm, R = 50 cm, and the angular speed of the larger wheel is 100 rpm, determine the angular speed of the smaller wheel in radians per minute.
What are the steps to solve this question?
1.Why does the angular speed of small gear depend only on larger gear only?
2.Why does the length of linkage connecting two gears does not have any influence on the angular speed of smaller gear?
The first question can be answered by looking at slack and tightening of chain caused by rotation...
Hello!
I have been brushing up my Rigid Body Dynamics.
I tried computing the angular speed with respect the Center of Mass (CM) using the usual split of kinetic energy and also the split of Angular momentum using the CM.
First, a simple case: Two particles of mass M each separated by a distance...
Hi all, I've been lurking around the forums for a while to get help with homework but I figured I'd finally make an account to get direct feedback.
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Homework Statement
13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ.
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Homework...
Homework Statement
Homework Equations
Angular momentum = moment of inertia * angular velocity
Change in angular momentum = impulsive moment
v^2=u^2+2as
The Attempt at a Solution
First I used v^2=u^2+2as to find the velocity of the particle the moment the string goes taut. I got v=\sqrt{8ag}...
Hey guys,
I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page:
So a couple of questions here:
(By the way, I know the answer is C)
1. My teacher explained that the net torque here on the assembly would be zero(will ask him again later). Is this...
Homework Statement
Mod note: Fixed thread title. OOPS NOT Acceleration, Speed! (Thread title is incorrect)
Homework Equations
w=d∅/dt
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I solved this with help from Chegg study, however, I'm still not entirely sure what I am doing. Obviously, for...
Homework Statement
A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees.
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The height of the outside wall of the house is...
Homework Statement
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Homework Statement
Homework Equations
...
The Attempt at a Solution
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In my textbook.In some question gives me angular speed as ( )rev/s.I know that its the frequency (f).But some questions It says angular velocity and says rad/s.
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Homework Statement
The 3.0 kg rod has a length of 80 cm. The 4.0 kg rectangle attached to the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal...
Homework Statement
A uniform thin circular rubber band of mass M and spring constant k has an original radius R. Now it is tossed into the air. Assume it remains circular when stabilized in air and rotates at angular speed ω about its center uniformly. Derive an expression for the new radius...
Homework Statement
A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds?
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wi= 65.0 rad/s
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Homework Statement
Homework Equations
Kinematic theorems:
The Attempt at a Solution
Ok, I'm trying to use another angle, phi, and find some relation betwen phi and theta so I can derive the equation for the angular velocity of rod B with respect to S, but I'm stuck at that point. How...
Homework Statement
Homework Equations
v=rω
conservation of energy
The Attempt at a Solution
I don't know whether it is correct or not, and I am quite confused in part b
it asks the angular speed of the pulley
can I say that v=rω since the pulley and box A,B have a common velocity?
so is ω...
Homework Statement
A particle of mass ##m## rotates about ##Z-##axis in a circle of radius ##a## with a uniform angular speed ##\omega##. It is viewed from a frame rotating about the ##Z-##axis with a uniform angular speed ##\omega_0##. Find the centrifugal force on the particle.
Homework...
Homework Statement
I have chosen my axis as you can see on the picture. To the left, it is the positive 'r'-axis, up is the positive 'y'-axis. I have to calculate the angular speed. My solution is correct, but I'm getting into trouble at the end. I have to take the roots of the last equation to...
Homework Statement
You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest...
Homework Statement
How do you calculate instantaneous angular speed?[/B]Homework Equations
I have been told that it is when delta t approaches 0, so its just the derivative of delta theta over delta t.[/B]The Attempt at a Solution
does it involve tangent line like normal instantaneous...
Homework Statement
Ok I have the answers to parts a and b, which I am 100% confident in since they are simple computations
Question is in attachement
a)74.9 rad/s
b)168.08 rad
My issue comes in when I have to get parts c
The mass of the cylinder is 8.7kg,
its diameter is .18m,
its .35m long...
Homework Statement
A ball rolls down an incline plane without slipping. What is the ratio of its angular velocity at h/3 to its angular velocity at 2h/3?
1) 1:2
2) 1:sqrt(2)
3) 1:1
4) sqrt(2):1
5) 2:1
Homework Equations
Conservation of energy with provisions for rotational and...
http://www.tech.plym.ac.uk/sme/mech226/gearsys/gearaccel.htm
Hello, I tried to derive n=N1/N2=omega2/omega1
with using T1=T2 but it is a wrong assumption.
I thought they should balance to satisfy Newton's 3rd law, but it is not.
Could you explain me why.
Homework Statement
Homework Equations
Vθ = r x θdot
Vr = rdot
Accelθ = r ⋅ θdot^2 + 2(r dot)(theta dot)
Accelr = r double dot - (r ⋅(θdot)^2)
The Attempt at a Solution
I know that the answer is supposed to be
But I'm not quite sure on how I'm supposed to get to an answer like that.
I'm...
Homework Statement
A wheel spins at an angular speed of 2.50 rad/s for a total of 30.0s. How many complete revolutions will the wheel make during this time?
A) 31.4 rev
B) 19.3 rev
C) 11.9 rev
D) 75.0 rev
Homework Equations
W=Wo+(alpha)(t)
θ=θo+Wot+1/2(alpha)t^2
W^2=Wo^2+2(alpha)(θ-θo)
The...