Finding Mean Angular Velocity of Rotating Body

AI Thread Summary
To find the mean angular velocity of a solid body with angular deceleration proportional to the square root of angular velocity, the initial angular velocity is denoted as ω0. The relationship between final angular velocity and time is expressed as ωf = ωi + βt, where β is the angular deceleration. To derive the mean angular velocity, integrating the angular velocity over time is necessary, leading to the result of ωavg = ω0/3. Clarification is sought on the integration process to arrive at this conclusion. Understanding the integration steps is crucial for solving the problem effectively.
paragchitnis
Messages
25
Reaction score
0

Homework Statement


A solid body rotates with deceleration about a stationary axis with an angular deceleration
\beta \propto \sqrt{\varpi} , where \varpi is the angular velocity. Find the mean angular velocity of the body averaged over the whole time of the rotation if at the initial moment of time the angular velocity was \varpi0

Homework Equations


\varpif = \varpii + \betat
\varpiavg = \varphi/t


The Attempt at a Solution


The given answer is <\varpi> = \varpi0/3
 
Physics news on Phys.org
, but I don't understand how to get there. We know that \varpif = \varpii + \betat, so we can integrate the expression \int_0^t (\varpii + \betat) dt. But then what?Can someone explain to me how to solve this?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

System of two wheels of different sizes with an axle through their centers
2
Replies
67
Views
4K
Angular Momentum Problem: Mouse walking on a rotating turntable
Replies
5
Views
1K
Sum of oscillating frequency and angular velocity
Replies
11
Views
2K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
7
Replies
335
Views
13K
Determine the angular velocity as a function of the angle
Replies
39
Views
3K
Existential dilemma on angular velocity of a complex rigid body
Replies
25
Views
2K
Brownian Ratchet (exercise framed by Feynman's Lectures, l. 46)
Replies
32
Views
2K
How to determine angular velocity about a certain axis?
Replies
10
Views
1K
Angular momentum of a rotating disc
Replies
3
Views
2K
Perfectly inelastic collision of two moving and rotating disks
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top