Question

A particle moving with an angular velocity of 200 Radian per second start the accelerating at a rate of 2 Radian per second square calculate the time in which it will come to rest

Answer 1

Here’s a general explanation of how to solve this kind of problem. The idea is to treat the units of measure as values, and manipulate them algebraically just like any other number.

Suppose we have a wheel that rotates 7 revolutions in one hour. This is expressed as a fraction:

speed=7revolutions1hourspeed=7revolutions1hour

Now suppose we want to find how many degrees per second it rotates.

There are 3600 seconds in 1 hour. Since these 3600 seconds = 1 hour, dividing one by the other equals 1:

1hour3600seconds=11hour3600seconds=1

Since multiplying anything by 1 doesn’t change it, we can write:

speed=7revolutions1hour×1hour3600secondsspeed=7revolutions1hour×1hour3600seconds

You can “cross-cancel” the 1 hour in this multiplication problem:

speed=7revolutions3600secondsspeed=7revolutions3600seconds

We know that a revolution is 360 degrees. Again, multiply by a fraction equivalent to 1:

speed=7revolutions3600seconds×360degrees1revolutionspeed=7revolutions3600seconds×360degrees1revolution

Cancel “revolutions”:

speed=73600seconds×360degrees1speed=73600seconds×360degrees1

speed=7×360degrees3600×1secondsspeed=7×360degrees3600×1seconds

speed=7×3603600degreessecondsspeed=7×3603600degreesseconds

speed=0.7speed=0.7 degrees per second.

Now you can do your homework problem the same way. Use:

1minute60seconds1minute60seconds and

2πradiansrevolution

Answer 2

since angular acceleration is constant, therefore we can use the following equation:

ω(final) = ω(initial) + α t

0 = 200 - (2)t .....(since ω is decreasing from 200 to zero, therefore α is negative)

t = 200/2

t = 100 seconds