Uniform circular motion of a rolling object

AI Thread Summary
To determine the number of revolutions a soccer ball makes while rolling 18 meters, first calculate the radius from the diameter of 33 cm, which is 16.5 cm or 0.165 m. Use the formula N = X / (2πr), where X is the linear distance traveled. The correct calculation gives approximately 8.68 revolutions, but ensure the radius is accurately used. The discussion emphasizes verifying the radius value to achieve the correct number of revolutions.
akatsafa
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A soccer ball of diameter 33cm rolls without slipping at a linear speed of 2.4m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 18m?

How do I just find the revolutions? I know how to use the equation to find rev/s, but how do I just get revolutions?

Thank you.
 
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Find out how long it takes for the ball to do a full revolution. Then find out how long it takes for the ball to move 18 metres. Divide the latter by the former and you should get your answer.
 
hint: there is superfluous information in the problem.
 
I'm using the equation N=X/2pi*r. When I do this, I'm getting 8.68 revolutions, but it's wrong. Is there another equation I should be using?
 
Nevermind. I know what I did wrong!
 
akatsafa said:
I'm using the equation N=X/2pi*r. When I do this, I'm getting 8.68 revolutions, but it's wrong. Is there another equation I should be using?
Your equation is correct. Be sure you are using the correct value for the ball's radius.
 
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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