course Phy 201
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22:29:28 `q001. Note that this assignment contains 4 questions. If an object rotates through an angle of 20 degrees in five seconds, then at what rate is angle changing?
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RESPONSE --> 20 degrees / 5 seconds = 4 degrees per second is the rate that the angle is changing.
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22:29:46 The change of 20 degrees in 5 seconds implies a rate of change of 20 degrees / (5 seconds) = 4 deg / sec. We call this the angular velocity of the object, and we designate angular velocity by the symbol `omega.
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RESPONSE --> ok
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22:30:49 `q002. What is the average angular velocity of an object which rotates through an angle of 10 `pi radians in 2 seconds?
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RESPONSE --> 10pi radians / 2seconds = 5 pi radians/second is the angular velocity.
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22:31:05 The average angular velocity is equal to the angular displacement divided by the time required for that displacement, in this case giving us `omega = `d`theta / `dt = 10 `pi radians / 2 seconds = 5 `pi rad/s.
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RESPONSE --> ok
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22:37:58 `q003. If an object begins with an angular velocity of 3 radians / sec and ends up 10 seconds later within angular velocity of 8 radians / sec, and if the angular velocity changes at a constant rate, then what is the average angular velocity of the object? In this case through how many radians this the object rotate and at what average rate does the angular velocity change?
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RESPONSE --> v0 = 3r/s vf = 8r/s 'dt = 10s average angular velocity: omega = 'd'theta / 'dt = (8r/s-3r/s) / 10s = 0.5radians / second 'ds = avg. vel * 'dt = (8r/s - 3r/s) / 2 = 2.5r/s * 10s = 25 radians is how many radians the object rotates
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22:39:48 Starting at 3 rad/s and ending up at 8 rad/s, the average angular velocity would be expected to be greater than the minimum 3 rad/s and less than the maximum 8 rad/s. If the angular velocity changes at a constant rate, we would in fact expect the average angular velocity to lie halfway between 3 rad/s and 8 rad/s, at the average value (8 rad/s + 3 rad/s) / 2 = 5.5 rad/s. Moving at this average angular velocity for 10 sec the object would rotate through 5.5 rad/s * 10 s = 55 rad in 10 sec. The change in the angular velocity during this 10 seconds is (8 rad/s - 3 rad/s) = 5 rad/s; this change takes place in 10 seconds so that the average rate at which the angular velocity changes must be ( 5 rad / sec ) / (10 sec) = .5 rad/s^2. This is called the average angular acceleration. Angular acceleration is designated by the symbol `alpha. Since the angular velocity in this example changes at a constant rate, the angular acceleration is constant and we therefore say that `alpha = `d `omega / `dt. Again in this case `d`omega is the 5 rad/sec change in the angular velocity.
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RESPONSE --> I accidentally subtracted the radians when averaging them instead of adding them together. That mistake through me off in my answer for the avg angular velocity, though I think my methods were correct.
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22:45:02 `q004. If an object starts out with angular velocity 14 rad/s and accelerates at a rate of 4 rad/s^2 for 5 seconds, then at what rate is the object rotating after the 5 seconds? Through how many radians will the object rotate during this time?
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RESPONSE --> 'omega (v0) = 14rad/s alpha (acceleration)= 4rad/s^2 'dt = 5sec vf^2 = 'omega^2 + 2alpha*'dt
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22:47:08 Changing angular velocity at the rate of 4 rad/s^2 for 5 sec the angular velocity will change by (4 rad/s^2) (5s) = 20 rad/s. Since the angular velocity was already 14 rad/s at the beginning of this time period, it will be 14 rad/s + 20 rad/s = 34 rad/s at the end of the time period. The uniform rate of change of angular velocity implies that the average angular velocity is (14 rad/s + 34 rad/s) / 2 = 24 rad/s. An average angular velocity of 24 radians/second, in 5 seconds the object will rotate through an angle `d`theta = (24 rad/s) ( 5 sec) = 120 rad.
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RESPONSE --> whoa I'm not sure that I could have been anymore off with my answer for this question. I read in the problem set 8 questions that the linear equations worked here, which is why I solved for vf and then 'ds in my answer.
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