Amass of 0.5 kg is whirled at 120 rpm in a horizontal circle at the end of a string 2 meters long. Neglecting the force due gravity, find: (a) the angular velocity (b) the centripetal acceleration.
angular velocity= 120rpm
Now if you want other units, convert, as here: 120rev/min *1min/60sec*2PI rad/rev
centripetal acceleration
a= m w^2 r
0.22
To find the angular velocity and centripetal acceleration of a mass whirled in a horizontal circle, we can use the following formulas:
(a) Angular velocity (ω) can be calculated using the formula:
ω = 2πn
where n is the number of revolutions per second. Since the problem states that the mass is whirled at 120 rpm, we need to convert this to revolutions per second:
n = 120 rpm * (1 min / 60 s) = 2 rev/s
Now, we can substitute this value into the formula to find ω:
ω = 2π * 2 rev/s = 4π rad/s
Therefore, the angular velocity is 4π rad/s.
(b) Centripetal acceleration (ac) can be calculated using the formula:
ac = ω^2 * r
where ω is the angular velocity and r is the radius of the circle. The problem states that the string is 2 meters long, so the radius would be 2m.
Substituting the values into the formula, we have:
ac = (4π rad/s)^2 * 2m
= 16π^2 m/s^2
Therefore, the centripetal acceleration is 16π^2 m/s^2.
To solve this problem, we need to calculate both the angular velocity and the centripetal acceleration. Let's tackle them one at a time:
(a) The angular velocity (ω) is the rate at which an object rotates around a fixed point. It is measured in radians per second (rad/s).
To find the angular velocity, we can use the formula:
ω = 2π * n
where ω is the angular velocity and n is the rotational speed in revolutions per minute (rpm).
Given that the object is rotating at 120 rpm, we substitute this value into the formula:
ω = 2π * 120
Calculating this expression gives us:
ω ≈ 753.98 rad/s
Therefore, the angular velocity is approximately 753.98 rad/s.
(b) The centripetal acceleration (ac) is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle.
To find the centripetal acceleration, we can use the formula:
ac = ω² * r
where ac is the centripetal acceleration, ω is the angular velocity in radians per second, and r is the radius of the circular path.
Given that the length of the string is 2 meters, the radius of the circular path is equivalent to 2 meters.
Substituting the values into the formula, we have:
ac = (753.98 rad/s)² * 2 m
Calculating this expression gives us:
ac ≈ 1,134,284 m/s²
Therefore, the centripetal acceleration is approximately 1,134,284 m/s².