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, we can use the following formulas:
Centripetal acceleration (a):
a = v^2 / r
Centripetal force (F):
F = m * a
Angular velocity (ω):
ω = v / r
Given:
Mass of the object (m) = 250g = 0.25kg
Radius of the circle (r) = 20cm = 0.2m
Speed of the object (v) = 12m/s
Let's calculate each value step by step:
1. Centripetal acceleration (a):
Using the formula a = v^2 / r, substitute the values:
a = (12^2) / 0.2
a = 144 / 0.2
a = 720 m/s^2
Therefore, the centripetal acceleration is 720 m/s^2.
2. Centripetal force (F):
Using the formula F = m * a, substitute the values:
F = 0.25 * 720
F = 180 N
Therefore, the centripetal force is 180 N.
3. Angular velocity (ω):
Using the formula ω = v / r, substitute the values:
ω = 12 / 0.2
ω = 60 rad/s
Therefore, the angular velocity is 60 rad/s.
In summary:
Centripetal acceleration (a) = 720 m/s^2
Centripetal force (F) = 180 N
Angular velocity (ω) = 60 rad/s