An object of mass 250g attached to the end of string is whirled round in horizotal circle of radius 20cm with a constant speed of 12m/s caleculate centipetal accelaration centripetal force angular velocity
To calculate the centripetal acceleration, centripetal force, and angular velocity of an object whirling in a horizontal circle, we can utilize the following formulas:
1. Centripetal acceleration (a):
Centripetal acceleration is the acceleration of an object moving in a circle at a constant speed. It is given by the formula:
a = v^2 / r
where v is the velocity of the object and r is the radius of the circle.
In this case, the velocity (v) is given as 12 m/s and the radius (r) is given as 20 cm. We need to convert the radius to meters by dividing it by 100:
r = 20 cm / 100 = 0.2 m
Now, we can substitute the values into the formula:
a = (12 m/s)^2 / 0.2 m = 144 m^2/s^2 / 0.2 m = 720 m/s^2
Therefore, the centripetal acceleration is 720 m/s^2.
2. Centripetal force (F):
Centripetal force is the force required to keep an object moving in a circle. It is given by the formula:
F = m * a
where m is the mass of the object and a is the centripetal acceleration.
In this case, the mass (m) is given as 250 g. We need to convert the mass to kilograms by dividing it by 1000:
m = 250 g / 1000 = 0.25 kg
Now, we can substitute the values into the formula:
F = 0.25 kg * 720 m/s^2 = 180 N
Therefore, the centripetal force is 180 N.
3. Angular velocity (ω):
Angular velocity is a measure of how fast an object rotates about a given axis. It is given by the formula:
ω = v / r
where v is the velocity of the object and r is the radius of the circle.
In this case, we already have the velocity (v) as 12 m/s and the radius (r) as 0.2 m. We can substitute the values into the formula:
ω = 12 m/s / 0.2 m = 60 rad/s
Therefore, the angular velocity is 60 rad/s.