Final answer:
Through an angle of 1280 degrees, a point on the edge of a pulley rotating at 320 revolutions per minute (rpm) moves in (2/3) of a second.
Step-by-step explanation:
The question involves calculating the angle rotated by a point on the edge of a pulley in a given time. The pulley is rotating at a rate of 320 revolutions per minute (rpm). To solve this, we will first convert the rotation rate into degrees per minute and then find out how many degrees are covered in (2/3) of a second.
We know that 1 complete revolution is 360 degrees. Therefore, if the pulley rotates 320 times per minute, it covers (320 revolutions/min) × (360 degrees/revolution), which equals 115200 degrees per minute.
Next, to find the degrees rotated in (2/3) second, we first convert 1 minute to seconds, which gives us 60 seconds. Therefore, 115200 degrees/min becomes:
(115200 degrees/min) ÷ (60 seconds/min) = 1920 degrees/second
Finally, to find the rotation in (2/3) second, multiply:
1920 degrees/second × (2/3) second = 1280 degrees
Thus, in (2/3) of a second, a point on the edge of the pulley moves through an angle of 1280 degrees.