The tape in a videotape cassette has a total length 219 m and can play for 2.4 h. as the tape starts to play, the full reel has an outer radius of 45 mm and an inner radius of 13 mm. at some point during the play, both reels will have the same angular speed. what is this common angular speed? answer in units of rad/s.

0.83 rad/s

Explanation:

As the plastic tape is coming off from 1 reel and then onto another reel, the rolling velocity of the 2 reels must be the same. For their angular speed to be the same, their radius must be the same as well since the rolling velocity is the product of angular speed and wheel radius.  

Let this radius be r, we know that 13 < r < 45 mm and r is somewhere so that the area of the donut-shaped object between 13mm and r is the same as the area of the donut-shaped object between r and 45mm

In math terms:  

where is the area at radius r, Ai and Ao are the inner and outer area of the empty and full reel, respectively  

or 0.03046 m

The rolling velocity of the cassette if it can play a total length of 219 m for 2.4 hours (2.4 * 60 * 60 = 8640 s)

v = 219 / 8640 = 0.02535 m/s

Therefore, the angular speed at both wheel is  

waves moving from a fast medium to a slow medium will experience a reflection as light travels more slowly than red light. total internal reflection occurs when the critical angle is.

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.