Final angular velocity of a mass on a pulley

AI Thread Summary
To determine the final angular velocity of a spool in a pulley system, Newton's 2nd Law and torque equations are applied. The sum of torques is calculated using the radius and force from the weight of the mass, leading to an angular acceleration of 20 rad/s². However, the calculated final angular velocity does not match the energy conservation approach, indicating a potential error in the tension analysis. It is crucial to consider the forces acting on both the bucket and the spool to accurately determine the tension in the string. Properly analyzing these forces will lead to the correct final angular velocity.
austindubose
Messages
17
Reaction score
0

Homework Statement


Use Newton's 2nd Law, sum of torques, and kinematic equations to determine the angular speed of the spool shown in the figure below. Assume the string has a negligible mass, and it turns without slipping. Use g=10 m/s2 for acceleration due to gravity.
1dzor5.png



Homework Equations


Ʃτ=rxF=Iα
F=mA
ωf2=ωi2+2αΔθ

The Attempt at a Solution


Sum of torques:
Ʃτ=rxf
=(.6m)(3kg*10m/s2)(sin 90°)=Iα
--> 18 kgm2/s2=Iα
α=18/[.5(5)(.62)]
α=20 rad/s2

But plugging this into the kinematic equation to solve for ωf doesn't give me the right answer (I know this because I calculated ωf based on conservation of energy first (ωf=11.01 rad/sec), so I think I may have messed up somewhere up until this point. Any suggestions?
 
Physics news on Phys.org
Do not assume that the force exerted on the spool equals the weight of the bucket. You need to figure out the tension in the string. (Analyze forces on the bucket as well as on the spool.)
 
Thank you! I knew it was something having to do with the tension. And I wasn't thinking of doing forces on both objects, more of just doing it as a whole.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Find the angular acceleration of the bridge?
Replies
1
Views
3K
Angular Acceleration of a Pulley with Mass
Replies
4
Views
13K
What is the angular acceleration of the rod?
Replies
18
Views
7K
What is the final angular velocity of each cylinder
Replies
1
Views
2K
ORBIT: change in orbital distance
Replies
10
Views
2K
How Does a Head Crash Affect Hard Drive Spin Dynamics?
Replies
1
Views
2K
Find velocities when a mass leaves a system of a rod with two masses
Replies
10
Views
2K
Frictional force (static) = 6 NSolved: Rotational Mechanics Homework
Replies
2
Views
3K
What is the relationship between angular momentum and angular velocity?
Replies
2
Views
2K
Calculating Time for Mass to Travel Distance on a Pulley
Replies
1
Views
11K

Hot Threads

Recent Insights

Back
Top