# What is Rotational acceleration: Definition and 29 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. ### Angle that makes kinetic and potential energy of simple pendulum equal

On the first attempt I used conservation of energy to get it down to a single equation involving theta and v (the speed when the angle is theta). But I had no idea how to find v. Now since the maximum speed is given, it is possible to find the maximum angular displacement, ##\alpha##. Then...
2. ### Forces when car wheels "lay rubber"

Suppose the car is moving to the right, so if the wheels roll without slipping, they are rolling clockwise. To get the wheel to slip, a counterclockwise torque would need to be applied to cause the wheel to have some angular acceleration. If the wheel was slipping, then the bottom of the wheel...
3. ### Torque required at the wheels to accelerate a vehicle at a certain rate?

I'm struggling to understand something basic here. If I have a just a wheel, with mass 10kg, and radius 0.25m, and I specify that the CG is accelerating linearly at 1ms-2, how do I calculate the force needed to do this? Using F = ma gives 10N, but using this value for torque calculation on the...
4. ### What is the rotational acceleration of a falling chimney?

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...
5. ### Problem 9.2 Classical Mechanics: Astronaut in a rotating space station

Homework Statement Acceleration experienced by an astronaut in a rotating space station. Homework Equations What force would he experience is his own rotating frame of reference. The Attempt at a Solution Newton's second Law for a rotating frame is: mr'' = F net+ Fcor + Fcf Fnet (In the...
6. ### Distance the hoop travels up the incline

Homework Statement A ring (hollow cylinder) of mass 2.61kg, inner radius 6.35cm, and outer radius 7.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=36.0°, as shown in the figure below. At the moment the ring is at position x = 2.19m up the plane, its speed is...
7. ### Calculating tangential acceleration of rotating object

Homework Statement An ant clings to the outside edge of the tire of an exercise bicycle. When you start pedaling, the an't speed increases from ) to 10 m/s in 2.6 s. The wheel's rotational acceleration is 13 rad/s^s. Determine the average tangential acceleration of the tire. Homework...
8. ### Find the linear acceleration of points on a rolling cylinder

Homework Statement [/B] A uniform cylinder with radius r is rolling down an incline without slipping as shown in diagram below. It's angular acceleration is α and acceleration of it's center of mass C is a. What will be the linear acceleration of point of contact P and another point Q on the...
9. ### How to find angular acceleration given a force applied?

1. The problem statement, all variables, and given/known data Joe is painting the floor of his basement using a paint roller. A roller has a mass of 2.4kg and a radius of 3.8cm. In rolling the roller across the floor, Joe applies a force F= 16N at an angle of 35 degrees. What is the magnitude if...
10. ### Solve Torque on Cylinder Homework Problem

Homework Statement A cylinder having a mass of 5.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure: F1 = 5.0 N, F2 = 6.0 N, F3 = 2.5 N, and F4 = 5.5 N. Also, R1 = 6.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the angular...
11. ### Atwood's machine with two connected discs

Homework Statement The system looks like this: I have two discs which are connected. Disc 1 has ##R_1##(radius) and ##M_1##(mass) Disc 2 has ##R_2## and ##M_2## ## R_2 > R_1 ## ## M_2 > M_1 ## on both discs weights are attached on opposite sides. On smaller ##m_1## is pulling and on bigger...
12. ### Torque and Rotational Acceleration

Homework Statement A 0.23-kg turntable of radius 0.31 m spins about a vertical axis through its center. A constant rotational acceleration causes the turntable to accelerate from 0 to 26 revolutions per second in8.0 s. Calculate the torque required to cause this acceleration. Homework...
13. ### Physics Lab Help - Moment of inertia and acceleration

Homework Statement In our physics lab we were to set up a system looking like this: where the mass was released and the velocity/acceleration and of the ring was calculated using MotionLab software. Our goal was to find the predicted total moment of inertia by just calculating the moment of...
14. ### Can I Tip a Can By Spinning a Weight? An Arduino Experiment

I want to be able to tip a can by building a device that fits inside the can and is able to tip it even when the can is completely closed. I have a motor and an arduino to control it. Would I be able to tip it by spinning a weight around the vertical axis of the can? Or would action and...
15. ### Rotational Acceleration of an Amusement Park Carousel

Homework Statement Moving at its maximum safe speed, an amusement park carousel takes 12 s to complete a revolution. At the end of the ride, it slows down smoothly, taking 3.5rev to come to a stop. What is the magnitude of the rotational acceleration of the carousel while it is slowing down...
16. ### Centripetal Force Washing Machine

I know that the centripetal force is the resultant force which points to the center. So in the case of a washing machine, what force pushes the clothes and water to the outer edge? There is not centrifugal force, but then how come all the clothes appear to get pushed to the circumference of the...
17. ### Bicycle Translational Acceleration vs Angular Acceleration

Homework Statement Given: Wheel radius is 20 CM, Gear radius is 5 CM, Coefficient of Static Friction is .2, Weight on rear wheel is 50 N. What is the minimum force that must be applied to the pedal for the wheel to begin accelerating on a level surface?Homework Equations Net T = I * a T = R X...
18. ### Force on rigid body: translation or rotational acceleration?

Homework Statement A perpendicular force F acts on the tip of a thin rod of length L and mass M in the ij-plane which is not fixed. What is the translational and rotational acceleration of the rod about the center of the rod? Homework Equations At first it seems like an easy problem...
19. ### Torque, force and rotational acceleration

This isn't a homework question. I'm really confused at this, say you're holding a massless ruler / stick and there is a mass (m) on it at a distance d from your hand. If you move the mass to 2d from your hand, would you have to apply twice the force as before, or quadruple to keep it stable? I...
20. ### Calculating Rotational Acceleration of a Wheel

Homework Statement A rotating wheel requires 3.05 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.05 s interval is 97.1 rad/s. What is the constant angular acceleration of the wheel?Homework Equations Well from basic calculus I know that acceleration is equal to...
21. ### Rotational acceleration of a post

[b]1. Hi, I am massively stuck on the following question and am examined on this stuff soon, could someone please help me? A thin, uniform 15kg post of length 1.75 m is held vertically using a cable attached to the top of the post. A string attached to a 5kg mass passes over a smooth, massles...
22. ### What Is the Rotational Acceleration in a Revolving Door?

Homework Statement Suppose a revolving door at the bank is spinning around once every 4 seconds. As you walk through, you push on the door for 3 seconds, which increases the rotational speed so that it rotates once a second. What wat the rotational acceleration due to your push? Homework...
23. ### How Do You Calculate Angular Acceleration in a Dual-Wheel Pulley System?

Homework Statement Two objects are attached to ropes that are attached to wheels on a common axle as shown below. The two wheels are glued together so that they form a single object. The total moment of inertia of the object is 41 kg·m2. The radii of the wheels are R1 = 1 m and R2 = 0.4 m. (a)...
24. ### Trying to derive the rotational acceleration.

Homework Statement Ok I'm trying to derive a=v^2/r Homework Equations The Boas book gives me two equations to start off with: r^2=\vec{r}*\vec{r}+constant and v^2=\vec{v}*\vec{v}+constant The Attempt at a Solution Where the hell did those equations come from. I know...
25. ### Rotational acceleration on merry go round

The rotational velocity of a merry go round increases at a constant rate from 0.6rad/s to 1.8rad/s in a time of four seconds. What is the rotational acceleration of the merry go round? This is what i have done so far but not too sure Time = 4seconds Change in velocity = 1.8rad/s –...
26. ### Understanding Rotational Acceleration: Linear vs. Angular Momentum Derivation

I'm getting confused with different types of acceleration when dealing with rotating systems. There is centripetal acceleration, tangential acceleration, and angular acceleration as far as i know. How do you derive that linear momentum equals angular momentum multiplied by the radius? And...
27. ### Rotational equilibrium, subtending, and rotational acceleration

The lightweight pivoted bar in Fig. MC8 will be in rotational equilibrium when a 200 N force acts none of these up at C only down at E or up at C up at B down at D (see attatched picture) So the net force has to be 0, i wasnt exactly sure how to do this one because i...
28. ### How does rotational acceleration affect different sized tires?

Hello, I'm hoping someone can help me understand the physics involved in a rotating object. Imagine 2 bicycle tires of different sizes with string wrapped around the rims. How would I describe or calculate which tire requires less force to start spinning, or the change in force necessary...
29. ### Need help quick with rotational acceleration

Imagine there is a bicycle wheel. At 1 point on the wheel a rope is fixed to the wheel. The rope is wrapped around the wheel 180 degrees and on the other end of the rope their is a weight (see image below). The point is actually that I want to compare the weight dropping from different...