# What is Angular acceleration: Definition and 567 Discussions

In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular acceleration, called spin angular acceleration and orbital angular acceleration respectively. Spin angular acceleration refers to the angular acceleration of a rigid body about its centre of rotation, and orbital angular acceleration refers to the angular acceleration of a point particle about a fixed origin.
Angular acceleration is measured in units of angle per unit time squared (which in SI units is radians per second squared), and is usually represented by the symbol alpha (α). In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise or decreases clockwise, and is taken to be negative if the angular speed increases clockwise or decreases counterclockwise. In three dimensions, angular acceleration is a pseudovector.For rigid bodies, angular acceleration must be caused by a net external torque. However, this is not so for non-rigid bodies: For example, a figure skater can speed up her rotation (thereby obtaining an angular acceleration) simply by contracting her arms and legs inwards, which involves no external torque.

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1. ### Angular acceleration of plank hanging off edge with a weight

Supposing L = 6m, m = 30kg, M = 70kg, h = 2m. Also set the origin at the leftmost edge of the plank. Free body diagram description: The center of mass of the plank is at ##\frac{L}{2}##, so considering it as a point mass, it feels the force of gravity ##F_m = mg##. The person is at some point...
2. ### Angular acceleration problem for a pulley used to raise an elevator

I tried to multiply 1/8 g (1.22625) by the radius (1.25 m) and got 1.53 rad/s^2. This is actually the linear acceleration of the elevator. How do I get the angular acceleration of the disk? Thanks!
3. ### Question involving clockwise angular movement

v=1.00*8=>v=8 rad/s ar=>100*8^2=>ar=64 rad/s^2 at=1.00*4=>at=4 rad/s^2 The only question I have is ar=-64 rad/s^2, not 64 rad/s^2 as I calculated. I believe this is because the wheel is accelerating in a clockwise direction. However this is not indicated by the mathematical equation. How do I...
4. ### Question involving angular acceleration of a spinning wheel

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?
5. ### Engineering How do I know that the angular acceleration is the same for both wheels?

how do I know that both angular accelerations are the same for both wheels here? should I apply relative motion analysis for the acceleration at A(with ##a_x,A and a_y,A##) and B(with ##a_{x,B} and a_{y,B}##) here, or is just a_A=r*alpha_C and a_B = r*alpha_D enough from which a_A=a_B and thus...
6. ### Motion with Time-Dependent Angular Acceleration

I am not understanding how to even start the question

8. ### Solving an Inertial Mystery: Angular Acceleration and Mud

So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall...
9. ### Engineering Calculating Angular Acceleration for Link BD and ED: Verifying Solution

Dynamics Rigid body Kinematics problem, looking for angular acceleration of link BD and ED. AB has constant angular velocity of 45 rad/s CCW. Could y'all verify any mistakes in my solution? Thanks!
10. ### The angular acceleration and period of a pulsar

for (a) ##T=\frac {2\pi}{\omega}## $$\omega=\frac {2\pi}{T}$$ $$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt}$$ $$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$ for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...
11. ### Engineering Calculating angular acceleration

I calculate the gravity force F = mg = (-9806.6)*(5.26e-1) = -5158 (mm^2*kg)/s^2 I get the moment M = F*r = (-3.5e5)*(-6.81e1) = 3.5e5 (mm^2 * kg) / s^2 Where r is the y coordinate distance from origin to centroid J = (Ix'...
12. ### I Non-Constant Angular Acceleration

Hello, I am trying to solve a problem involving a mass with known moment of inertia about an axis with a lever arm at angle theta and length r with a non-constant spring force acting at the tip of the lever arm and fixed distance away from the axis of rotation. I am wondering what the best...

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14. ### Engineering Rigid wheel rolling without slipping -- Trying to find angular acceleration

So I tried the problem and it’s different from the solution. I’m confused on why my attempt didn’t work, is it because the wheel is undergoing general planar motion? I tried to just apply Newton’s 2nd law to find the acceleration of the centre and then use that to find angular acceleration. The...
15. ### Getting the angular velocity using the angular acceleration graph

The answer here is A What i did is getting the area as follows, 2×4×1/2 +3×-6×1/2 +4×-6 = -29 and then use this Δω=ωf-ωi -29=ωf-5 ωf=24 but there is no such choice.
16. ### Describe the motion of yoyos suspended from the ceiling

I have trouble solving this problem any help would be appreciated.Problem statement ##J=\frac{mr^2}{2}## a) Determine the motion of yoyos for ##n=1,2,3## The case for ##n=1## is simple, however, I am having trouble with ##n=2## and ##n=3##. for ##n=2## I started by drawing all the forces...
17. ### Angular Momentum Problem: Determining Angular Acceleration

So I first tried to find L using torque, Torque=d/dt*L, and took the integral of this. Ended up with 23.28484t Now I square the equation L=rotation rate*I to get L^2=rotation acceleration *I^2 Angular acceleration=L^2/I^2 I feel like I am doing something wrong though, this doesn't give the...
18. ### What's the angular acceleration?

##\tau## = 0.5*mg ##\alpha##= (0.5mg)/##mr^2## This is what I'm finding difficult to understand, if a particle is in linear translation, how can it have angular acceleration. If by calculation, angular acceleration is non-zero, then shouldn't the body must move in a circular path with...
19. ### Find the angular acceleration of two reflectors attached to a rod

Okay so I actually have the answer because my teacher basically just gave it to me, but I would really like to know why I was even wrong in the first place. Here's my steps: 1. Knowing the momentum transfer per unit area is described by: 1/A dp/dt = S/c. I can begin by relating some known...
20. ### Angular velocity and angular acceleration of a turbine

Okay so what I've done; I've put the diammter d = 1m as r = 1m The time interval of 4s is t = 4s and the angular velocitys as; ω1 = 20 rad/s ω2 = 40 rad/s Now to get the accelaration. Angular acceleration can be split into two parts tangetial acceleration and radial acceleration What I...
21. ### Angular acceleration calculation

Torque=225 Ncm Torque=α*0.35 kg.cm² α=225Ncm/0.35kg.cm² =225 kg.m/s²*cm/0.35kg.cm² =225*100/.35s² =64285.7/s² but the answer is wrong
22. ### Why is there angular acceleration in a non-spinning gyroscope?

I was watching the above video which is part of a series explaining the mechanics behind a gyroscope. In the video the author explains the mechanics of the gyroscope when stationary (the disc is not rotating). Here he derives a result that the angular acceleration is g/r which is non zero...
23. ### Exploring Moment of Inertia & Angular Acceleration for Drone Propellers

Hi, I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...
24. ### Finding the angular acceleration of a flywheel

I have solved part a using the conservation of energy, getting a (correct) answer of 47.9 km/h, but I am unable to make headway with part b. Based on the flywheel rotating at 237rev/s when the car is moving at 86.5 km/h, I obtained omega = (237*2pi)v/24=62v. Differentiating both sides should...

26. ### Angular Acceleration: Understanding the Relationship Between Connected Pulleys

Hi everyone I had this argument with someone told. About angular acceleration. His opinion: Since both pulleys are connected by a string then both of them must have the same angular acceleration. My opinion: Since a2 "acceleration of the second mass" is half a1. Then angular acceleration of the...
27. ### How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

total moment of inertia= (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.016kg) (0.01m)^2 total moment of inertia= 2.03*10^(-3) kgm^2 torque= 5.2N * (0.144m) = 0.75N*m thus: 0.75N*m= 2.03*10^(-3) kgm^2 * angular acceleration angular acceleration = 368.8 rad/s^2 Is...
28. ### Angular speed, acceleration, and angle of a Ferris wheel

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...

30. ### Rotational Motion and moments of inertia

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...
31. ### Spinning objects and angular acceleration

I believe I know that when an object, in terms of linear motion, accelerates, it is being resisted by inertia, thus creating so called fictitious forces. Now, that said, how does angular acceleration affect spinning objects like say, a gymnast, when they spin around the axis of rotation? Do they...
32. ### Dynamics: Angular Acceleration Problem

Both point A and B are moving in parallel in same direction, therefore rod is not rotating at this instance and angular acceleration is 0. Question states angular velocity is equal to zero. Plugging into Angular Acceleration"AB" = r*sqr(angular velocity"AB") = 0.26m* sqr(0) = 0 [Moderator's...
33. ### Rotating with slipping to rotating without slipping?

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.
34. ### Rotating Sphere: Conceptual Question

As shown in figure there's a homogeneous solid sphere. It is rotating about axis which is passing through point P directed perpendicular to the plane of paper. (In short like a pendulum). I'm neglecting gravity and assuming a force F which is directed perpendicular to the string. (The string...
35. ### Rotating Disk and Hanging Mass Calcululations

I used the above equations to solve for tension, torque, inertia, and angular acceleration. Are the formulas I used correct for the given system? How can I calculate Inertia from the trendline equation, I'm drawing a blank.
36. ### What is the angular acceleration of this cylindrical system?

PART B ONLY: The cylinder undergoes torque when the mass m2 is removed: τNET = Iα = FNETr = 45α = FT(0.5) FT = 90α, therefore msystem = 90 kg After this step, I am not sure what to do. τ = ΣF = Fg - Ft = ma = (20 kg)(9.8 m/s2) - (90α) = 196 -...
37. ### How to calculate angular speed?

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...
38. ### Circular Motion With Constant Angular Acceleration

Homework Statement Question: A 600 g steel block rotates on a steel table while attached to a 1.20 m-long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 5.01 N perpendicular to the tube. The maximum tension the tube...
39. ### Calculus angular acceleration with respect to theta

Homework Statement A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ2/3)rad/s2 , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s. Homework Equations α =...
40. ### Rotational Motion: Average angular acceleration of a CD

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...
41. ### Radial Acceleration in Polar/Cylindrical Coordinates

My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ? If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...
42. ### Automotive Calculating the angular acceleration of a swivel seat

We have an automotive swivel seat that turns from the initial seating position to the final position outside the vehicle (90 degree swivel in 15 seconds). We would like to calculate the torque required for rotating the seat along with the person. We have calculated the inertia of the movable...
43. ### Max ω of circular hoop rotating around a peg and oscillation

Homework Statement Homework Equations F=ma τ = Iα = rF v=rω, a=rα L = Iω Center of Mass/Moment of intertia equations The Attempt at a Solution [/B] So right now I've tried to model the force acting on the ring as it goes around the peg, but I think centripetal force is involved and I'm not...
44. ### Finding the coefficient of kinetic friction on an incline

<< 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...
45. ### Wheel-Hub System and Angular Acceleration

Homework Statement A wheel of radius r1=0.8m and hub of radius r2=0.4m is shown in the diagram. Two masses are hung from the wheel-hub system. The mass m2, on the left, is hung from the hub. The mass m1 is hung from the wheel. The system is in equilibrium. The moment of inertia for the disk-hub...
46. ### Translational + Angular Acceleration of Free Body (not fixed)

Imagine a long brick in outer space. You apply a force tangential to the center of mass. The brick accelerates in a transitional and angular fashion. There are no constraints or fixed axis. How would I calculate the translational and angular acceleration? I would like to run some simulations...
47. ### Angular Acceleration Homework: 962 Revolutions in 10 Secs

Homework Statement A computer disk starts from rest, then speeds up with angular acceleration of 190 rad/s^2. until it reaches its final speed of 7200 rpm. How many revolutions will it have made 10.0 secs after starting up? Homework Equations w = w0 + at rps = rpm / 60 1 rev = 2*pi rad 1 rad =...
48. E

### Torque on Rod Due to Normal Force at a Hinge

Homework Statement In this diagram, I wondered if there is any torque due to the normal force from the hinge, once the support stick is removed. I also want to know what the normal force would be at the hinge. The cup and ball are to be ignored here (essentially massless). Homework Equations...
49. T

### How to solve for the moment of inertia and angular acceleration?

A girl is climbing up a set of stairs and has her femur horizontal. Her thigh weighs 12 pounds, acting at a center of mass 15 cm from her hip joint. She places 50 pounds of weight on the lower portion of that leg, vertically through her knee. Her gluteus maximus is applying a force directed 30...
50. ### What is the angular acceleration of the rod?

Homework Statement A thin, uniform, 18.5 kg post, 2.10 m long, is held vertically using a cable and is attached to a 5.00 kg mass and a pivot at its bottom end (as shown below). The string attached to the 5.00 kg mass passes over a massless, frictionless pulley and pulls perpendicular to the...