Transcript for:
Circular Motion and Speed Calculations

okay the diagram shows an electron undergoing uniform circular motion so uniform cycle motion means moving around at a constant speed in a circle the radius of orbit is 1.5 nanometers calculate the distance moved by electron when it on when it goes to an angular displacement of 40 degrees so angular displacement of the angle is turned through okay it's represented by Theta here okay it's normally actually measured in radians so here we've got in degrees we're going to turn that into radians soon we're trying to calculate the distance traveled or the arc length in this case s there okay that's linked by this equation s which is arc length in meters or the distance in this case and R is the radius of the orbit or rotation measured in meters and then Theta which diagonal displacement again in radians so instead of 40 degrees into radians so 40 degrees divided by 360 and then Times by the equivalent of 360 in radians which is 2 pi and that gives us 0.70 radians and then we can do the displacement here or sorry that this is moved equals the radius which I'm turned into meters from nanometers times angle and that gives us the distance move which is 1 times the power minus 9 meters the geode station is Select this uniform circular motion around the earth with a time period of 24 hours so time period means the time it takes one orbit one cycle one revolution you would have come across this term in the waves topic which where where it stood for the time it takes for one complete wave here just means the time it takes one complete cycle of anything really okay the radius of orbit is given in kilometers we also calculate the speed of the satellite so speed is distance divided by time so in this uh SCA you could use ARC language R Theta but we're given the time period which is capital T so in one time it is going to be one whole rotation so we know it's going to travel the circumference of this circle the circumference is 2 pi r so we can put that instead of R Theta here so we put 2 pi r here we get this equation very important equation the speed equals 2 pi r which is the circumference divided by a time period the time it takes to do that so in this case 2 times pi and I've turned the gray radius in from meters to kilometers so from kilometers to meters divided by time that's 24 hours I'm going to turn that into 60 minutes Times by 60 seconds and that gives me a speed of 3770 meters per second okay gear in a car is rotating at 300 revolutions per second so 300 revolutions per second that's like saying how many rotations per unit time or number of oscillations per unit time it's basically the frequency okay so in fruit in the waves topic you would have seen that as the number of waves per unit time here which is doing normal rotations orbits per unit time so that's frequency is 300 Hertz because Hertz is the number of waves or oscillations per second okay so the diameter the disk is given and we'll calculate the speed on the edge of the disk so we just saw the equation for Speed which is a circumference divided by time period now we also know the time period is one over frequency so if we put that in we get this equation here and I'm just going to put the numbers in here I've got 2 pi r I've turned from centimeters into meters I've divided diameter by two as well and then I've Times by The Frequency to get my speed of 113 meters per second