course Phy 201 áMçé{ÿѲýª¾{ñÐýâ¡ãeÑwassignment #030
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13:08:24 `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 --> We take the change in angle and divide by `dt we get 20deg/5s=4deg/s confidence assessment: 3
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13:08:41 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 self critique assessment: 3
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13:13:21 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 --> Since average angular velocity is equal to angular displacement divided by time we can say 10 pi rad/2s=5 pi rad/s self critique assessment: 3
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13:18:32 `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 --> If we take (8rad/s+3rad/s)/2=5.5rad/s. If the object rotates for 10secs then we have distance of 5.5rad/s*10s=55 rad. The angular acceleration will be (8rad/s-3rad/s)/10s=.5rad/s^2 confidence assessment: 3
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13:19:07 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 --> ok self critique assessment: 3
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13:27:12 `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 --> Since we rotating with an alpha of 4rad/s^2 for 5 s then our change in angular velocity would be 4rad/s^2*5s=20rad/s. Since our intial angular velocity was 14rad/s and we have a change of angular velocity of 20rad/s then our final angular velocity is 14rad/s+20rad/s=34rad/s. Our average angular velocity will be (14rad/s+34rad/s)/2=24rad/s. 24rad/s for 5s =120rad confidence assessment: 3
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13:27:42 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 --> ok self critique assessment: 3
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