How Do You Calculate Arc Length and Angle Measurements in Circular Motion?

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To calculate arc length and angle measurements in circular motion, the distance between marks on a protractor can be determined by understanding the relationship between the radius and degrees. A protractor with a 7.5 cm radius has marks spaced according to the angle in degrees, but the initial calculation of 360/7.5 is incorrect. For a phonograph record with a 12-inch diameter, a quarter turn corresponds to pi/2 radians. To find the distance a point on the rim has moved, one must calculate the circumference using the formula C = 2πr, where r is the radius. Understanding these concepts is essential for accurate measurements in circular motion.
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A protractor is made so that the edge of its scale is 7.5 cm from the center point. If the scale is marked in degrees, how far apart are the marks along the edge?

I just thought this would be 360/7.5 but it's not. I'm not sure If I got the question correct.





A 12-inchdiameter phonograph record rotatesaboutits center by one-quarter turn. a) Thorugh how many radians has it turned? b) How far has a point on the rim moved?

For a, I got pi/2 which I think iscorrect, but for b, I don't know what to do...
 
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can i get some help?
 
What is the circumference of a circle in terms of its 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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