If we assume an object is continuously rotating, then another way to look at rotational motion is to examine the period of rotation, T. Measurable in units of time ( milliseconds, second, hours, years, eons…) the period is how much time is takes to make one complete rotation. We could also describe how frequently the object rotates. The frequency, f, of an object is actually the inverse of the period of rotation. The metric unit for frequency is Hertz ( Hz), where 1 Hertz = 1 cycle/second. You are probably familiar with the term Hertz from frequencies on the radio dial such as WBUR 90.9 MHz or WBZ 1030 kHz.
If he spins at a frequency of 0.8 Hz, how much time does it take him to make 1 rotation? Imagine a small boy tries to make himself dizzy by spinning around rapidly. T = 1/f = 1/0.8 Hz = 1/0.8 cycles/second = 1.25 secondsĪnother traditional unit for frequency is revolutions per minute or rpm. You might see this on an old fashioned record player which could rotate at 33 or 45 rpm.įor now consider two little LEGO men standing on a record player. As the record player turns, we can describe the motion of the little LEGO men in terms of their linear speed (meters/second) or their rotational speed. If we set the record player to 45 rpm, then both LEGO men have the same rotational speed. We can calculate the linear speed for each man using the equation We use the word tangential because if the LEGO man were to slip and fall, his own inertia cause him to fly off the record player on a line tangent to his circular motion! However, they have different linear or tangential speeds.
Where r is the radius of the circle and T is the period of rotation. In this case, the distance for one period of rotation happens to be the circumference of a circle. If the men are located on our record player at positions 10 cm and 4 cm from the center axis: Exampleįirst we calculate the period. V= 2πr/T = 2π (10 cm)/ 1.33 sec = 47 cm/sįor the little man who is standing at radius of 4 cm, he has a much smaller linear speed although the same rotational speed Thus the period of rotation is 1.33 seconds. We can define the relationship between linear velocity and angular velocity with the following equation There is a subtle difference between rotational speed and rotational velocity, which we will introduce at a later time. Notice, that ω, the angular velocity, was defined earlier as the change in angle per unit time.Įxamining the above equation there is an interesting question as to the units for angular velocity.
Up until now we have used terms such as revolutions per minute or rotations per second. But a revolution would be defined as one COMPLETE turning through 360°. You have probably studied the units for angles in terms of degrees. But when we discuss angular velocity we usually are not talking about an integral number of rotations. Thus we could have to use units such as degrees/second. However, the degree is not the metric unit of rotation. The standard unit is actually the radian. If we look at a picture of a unit circle we can see the conversion between radians and degrees. They are really the same thing, just different units. In one sense, the only difference between frequency and angular velocity is a matter of units.
Thus we could express an algebraic relationship between these two terms as Angular velocity is measured in radians/second and frequency is measured in Hertz or rotations/second. Using this, we could actually find the angular velocity of our record player which spins at 45 rpm. Let us revisit the LEGO men on the record player.This product is designed, manufactured and shipped from the USA. The Falcon Power Supply Unit from Phoenix Engineering is a microprocessor controlled digital AC power source, used for accurate speed control of a turntable motor.
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