Festive of Lights!
A lamp is attached on circumference of a horizontal disc that is sliding on a frictionless horizontal floor in a dark room. The lamp emits sharp light pulses of different colours at regular interval of ß = 1.00 s . Colours of the pulses repeatedly change in a sequence red >green> yellow>blue. Center of mass of the lamp , its power supply and the disc coincide with the center of the disc. In a particular interval locations of four pulses observed is as followed Red at (4,10) , Green at (1,5) , Yellow at ( 8,0) , Blue at (15,5) ( All x and y coordinates are in cm. If radius of disc is R , velocity of centre is V and angular velocity of disc is ø . Then find R×V×ø .( in cm , cm/s and rad/s. Only take magnitudes)
The answer is 15.708.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Displacement ∆r of the lamp between two consecutive pulses can be represented by the vector sum of two components . One due to displacement of center of the disc and other due to intrinsic rotation of disc.
∆r= V× ß + 2R sin(øß/2)ê
ê is the unit vector in the direction of displacement of lamp w.r. to the center of disc between two consecutive pulses.
Now take a look at the pic .