Angular Velocity: Find Initial Velocity Given Acceleration & Displacement

AI Thread Summary
A wheel experiences a constant angular acceleration of π rad/s² and an angular displacement of π rad, with a final angular velocity of 2π rad/s. The challenge is to determine the initial angular velocity, given that the time interval is unknown. The relevant equation is w² = Wo² + 2αΔθ, which relates initial and final velocities, angular acceleration, and displacement. The discussion emphasizes the simplicity of the problem due to the constant acceleration. Participants express hope for easier exam questions in the future.
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Homework Statement



a wheel rotates with a constant angular acceleration pie rad/s^2. during a certain time interval its angular displacement is pie rad. at the end of the interval its angular velocity is 2pie rad/s. what is the angular velocity at the beginning of the interval?

Homework Equations



tried looking at the angular velocity/displacement/acceleraions equations but i don't know how to even begin this question.

The Attempt at a Solution



well i have to find the initial angular velocity and the time interval is also unknown.
 
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In the problem angular acceleration, angular displacement and final velocity is given. Can you find an equation which contain initial velocity, final velocity, angular acceleration and angular displacement.
 
yes but it also has time, which is uknown.
 
Lol at U of M exam questions ;). This one's simple, the key is constant acceleration.

w^2 = Wo^2 +2(alpha)(deltatheta) should do the trick ;)
 
lol jegues thanks.
hope the exam will be simpler than that haha
 
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}...
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