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. 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. 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. In this case, the distance for one period of rotation happens to be the circumference of a circle. Where r is the radius of the circle and T is the period of rotation. 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. If we set the record player to 45 rpm, then both LEGO men have the same rotational speed. 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. 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. 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. 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. You are probably familiar with the term Hertz from frequencies on the radio dial such as WBUR 90.9 MHz or WBZ 1030 kHz. The metric unit for frequency is Hertz ( Hz), where 1 Hertz = 1 cycle/second. The frequency, f, of an object is actually the inverse of the period of rotation. We could also describe how frequently the object rotates. Measurable in units of time ( milliseconds, second, hours, years, eons…) the period is how much time is takes to make one complete rotation. If we assume an object is continuously rotating, then another way to look at rotational motion is to examine the period of rotation, T.

We also can have rotational kinetic energy! Frequency and Period Building on that, angular momentum is rotational inertia in a state of rotational motion.

The moment of inertia (or rotational inertia) is the tendency for an object to stay at rest or stay in a state of rotational motion. We can examine torque, which is a rotational force. There is also an angular acceleration which is the rate of change of the angular velocity. Has its rotational analogue, the rotational velocity, the rate of change of angle Likewise, the velocity of an object or the rate of change of position We could also rotate an object through an angle θ. In the beginning of the year we discussed how an object could undergo a displacement x.

We are now going to begin to explore rotational motion.Įvery concept we have studied so far has a rotational analogue. So far this semester in our study of classical mechanics we have studied translational motion.

Rotational motion