A point on a wheel moves at 32π/9 radians per minute.
How many seconds are required for the point to complete 7 revolutions?
Enter your answer, rounded to the nearest tenth,
32pi/9 R/min / 60 sec/min = .186168 R/sec
7 rev = 14 pi Radians
14 pi R / .186168 R/sec = 236.25 sec
A point on a wheel moves at 32π/9 radians per minute.
How many seconds are required for the point to complete 7 revolutions?
Enter your answer, rounded to the nearest tenth,
Convert rotation speed to radians per second 32 π rad 1 min 32 π rad
—— —— x — —— = ——— ——
9 min 60 sec 540 sec
1 revolution equals 2 π radians, so
7 revolutions equals 14 π radians,
and the question becomes how long
does it take to turn 14 π radians distance (the distance is 14 π radians)
time = ————
rate (the rate is the rad/sec determined above)
To divide by a fraction, you invert
the divider and multiply. 14 π radians 540 sec
Note that π and radians cancel time = —–— ——— x ——— ———
1 1 32 π radians
14 x 540 sec
time = ——–—— —— = 236.25 sec rounds to 236.2 sec
32 1
.