A UNIFORM DISC 6.00CM IN RADIUS ROTATES AT A CONSTANT RATE OF 1200REV/MIN ABOUT ITS CENTRAL AXIS.DETERMINE ITS ANGULAR SPEED AND THE TOTAL DISTANCE A POINT THE RIM MOVE IN 3.00S.
Va = 1200rev/60s * 6.28rad/rev = 125.6 rad/s = Angular velocity.
Circumference = pi*2r = 3.14 * 0.12m = 0.377 m.
d = 1200rev/60s * 3s * 0.377m/rev = 22.6 m.
1200rev/min * 2π/rev * 1min/60s = 40πHz
40πHz * 3s = 120π*6cm = 720πcm
To determine the angular speed of the uniform disc, we need to convert the given rotation rate from rev/min to rad/s.
Angular speed (ω) is given by the formula:
ω = (2π * n) / t
where ω is the angular speed in rad/s, n is the number of revolutions, and t is the time in seconds.
Given:
Rotation rate = 1200 rev/min
To convert rev/min to rad/s, we need to consider that there are 2π radians in one revolution and 60 seconds in one minute.
Number of revolutions (n) = 1200 rev/min
Time (t) = 1 min = 60 s
ω = (2π * 1200) / 60
= 40π rad/s
≈ 125.66 rad/s (rounded to two decimal places)
Therefore, the angular speed of the uniform disc is approximately 125.66 rad/s.
To determine the total distance a point on the rim moves in 3.00 seconds, we need to use the formula:
Distance (s) = ω * r * t
where s is the distance, ω is the angular speed in rad/s, r is the radius of the disc, and t is the time in seconds.
Given:
Radius (r) = 6.00 cm
Time (t) = 3.00 s
s = 125.66 rad/s * 6.00 cm * 3.00 s
= 2257.88 cm
≈ 22.58 m (rounded to two decimal places)
Therefore, the total distance a point on the rim of the disc moves in 3.00 seconds is approximately 22.58 meters.