Improve Your Test Review: Solving for Final Angular Speed with a Spinning Mass

  • Thread starter Thread starter fishingaddictr
  • Start date Start date
  • Tags Tags
    Review Test
AI Thread Summary
To solve the problem of finding the final angular speed of a mass connected to a cord, the principle of conservation of angular momentum is applied. The initial parameters include a mass of 1.32 kg, a cord length of 1.62 meters, and an initial angular speed of 8.0 radians per second. When the cord is pulled inward to 0.33 times its original length, the relationship r1^2*v1 = r2^2*v2 is used to determine the final angular speed. The calculations suggest that the final angular speed is 73.46 radians per second. This approach effectively demonstrates the conservation of angular momentum in a rotating system.
fishingaddictr
Messages
16
Reaction score
0
im stuck on one of the homework problems I am reviewing for a test. any help would be appreciated. I am not sure on how to set up the problem.

a small 1.32 kg mass is connected to a cord of length 1.62 meters, and spun at a constant angular speed of 8.0 radians per second. if the cord is pulled inward so that the mass is only 0.33 times as far from the axis as it started out, what is the final angular speed of the mass at its new distance from the axis?
 
Physics news on Phys.org
HINT: Conservation of angular momentum
 
thats what i was thinking.. so i would set them equal.. what would the moment of inertia be for this case?
 
Since the mass is small, I = mr^2, where r is the length of the cord.
 
oh ok. i got it

since the mass would cancel out i got r1^2*v1=r2^2*v2 with the answer 73.46radians per second.

is that correct?
 
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

Angular Momentum Problem: Mouse walking on a rotating turntable
Replies
5
Views
1K
An equilibrium problem -- Spinning a hinged rod and a ball
Replies
21
Views
3K
How Does an Impulse Affect the Angular Momentum of a Spinning Wheel in Space?
Replies
6
Views
1K
Calculating Final Angular Speed of a Rotating Disk with a Horizontal Axis
Replies
8
Views
3K
Angular velocity tank receiving cereal
Replies
3
Views
2K
Angular Speed And Kinetic Energy
Replies
17
Views
7K
Analyzing an Angular Impulse Problem
Replies
12
Views
2K
A solid disk of radius 23.4cm and mass 1.45kg....
Replies
3
Views
1K
A student holding weights angular momentum problem
Replies
5
Views
2K
Solving for inertia and angular speed
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top