Question

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make

Answer 1

Answer:

37.5 revolutions

Step-by-step explanation:

The average rotation speed for the first second and for the last two seconds is:

$V_1 = \frac{0+500}{2}\\ V_1 = 250\ rpm$

For the next 3.0 seconds, the rotation speed is V = 500 rpm.

The total number of revolutions, converting rpm to rps, is given by:

$n=\frac{1*V_1+3*V+2*V_1}{60}\\n=\frac{1*250+3*500*2*250}{60}\\n=37.5\ revolutions$

The DVD makes 37.5 revolutions.