An object of mass 250g attached to the end of string is whirled round in horizontal circle of radius 20cm with a constant speed of 12m/s calculate centripetal accelaration centripetal force angular velocity
To calculate the centripetal acceleration, centripetal force, and angular velocity, we can use the following formulas:
1. Centripetal acceleration (a):
The formula to calculate centripetal acceleration is given by a = v^2 / r,
where v is the velocity and r is the radius of the circular path.
2. Centripetal force (F):
The formula to calculate centripetal force is given by F = m * a,
where m is the mass of the object and a is the centripetal acceleration.
3. Angular velocity (ω):
The formula to calculate angular velocity is given by ω = v / r,
where v is the velocity and r is the radius of the circular path.
Now, let's calculate the values:
Given:
Mass (m) = 250 g = 0.25 kg
Velocity (v) = 12 m/s
Radius (r) = 20 cm = 0.2 m
1. Centripetal acceleration (a):
Using the formula a = v^2 / r, we can substitute the values:
a = (12 m/s)^2 / 0.2 m
a = 144 m^2/s^2 / 0.2 m
a = 720 m/s^2
2. Centripetal force (F):
Using the formula F = m * a, we can substitute the values:
F = 0.25 kg * 720 m/s^2
F = 180 N
3. Angular velocity (ω):
Using the formula ω = v / r, we can substitute the values:
ω = 12 m/s / 0.2 m
ω = 60 rad/s
Therefore, the centripetal acceleration is 720 m/s^2, the centripetal force is 180 N, and the angular velocity is 60 rad/s.