A wheel of arduous 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. Through what angle, in radians, does the wheel rotate in 1.0 s? What is the linear speed of a point on the wheel's rim? What is the wheel's frequency of rotation?
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To find the angle through which the wheel rotates in radians, we need to know the number of revolutions the wheel makes in one second, and then convert it to radians.
Given that the wheel rotates at a rate of 2.0 revolutions every 0.080 s, we can calculate the number of revolutions per second:
Revolutions per second = 2.0 revolutions / 0.080 s = 25 revolutions/s
We know that one revolution is equal to 2π radians, so to find the angle in radians, we can multiply the number of revolutions per second by 2π:
Angle in radians = 25 revolutions/s * 2π radians/revolution = 50π radians/s
Therefore, the wheel rotates through an angle of 50π radians in 1.0 s.
To find the linear speed of a point on the wheel's rim, we need to calculate the distance traveled by a point on the rim in 1.0 s. The distance traveled can be found using the formula:
Distance = Circumference of the wheel * Number of revolutions
The circumference of the wheel is given as 30 cm. Since the wheel makes 2.0 revolutions in 0.080 s, we can use this to calculate the linear speed:
Distance = 30 cm/revolution * 2.0 revolutions/0.080 s = 750 cm/s
Therefore, the linear speed of a point on the wheel's rim is 750 cm/s.
The frequency of rotation is the number of complete rotations per unit of time. In this case, the wheel makes 2.0 revolutions in 0.080 s. To find the frequency, we can use the formula:
Frequency = Number of revolutions / Time
Frequency = 2.0 revolutions / 0.080 s = 25 Hz
Therefore, the wheel's frequency of rotation is 25 Hz.