a body of mass 6kg is whirled in a horizontal circle of radios 1.5m with a uniform velocity 3m/s. calculate 1. the angular velocity 2. the centripetal acceleration.
C = 2pi*r = 6.28 * 1.5 = 9.42m.
1. Va = 3m/s * 6.28rad/9.42m = 2rad/s.
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To calculate the angular velocity and centripetal acceleration, we can use the formulas:
1. Angular velocity (ω) = v / r
2. Centripetal acceleration (aᵣ) = ω² * r
where:
- v is the linear velocity of the object
- r is the radius of the circle
Given data:
- Mass of the body (m) = 6 kg
- Radius of the circle (r) = 1.5 m
- Linear velocity (v) = 3 m/s
Now, let's plug in the values into the formulas:
1. Angular velocity:
ω = v / r
= 3 m/s / 1.5 m
= 2 rad/s
Therefore, the angular velocity of the body is 2 rad/s.
2. Centripetal acceleration:
aᵣ = ω² * r
= (2 rad/s)² * 1.5 m
= 4 rad²/s² * 1.5 m
= 6 m/s²
Therefore, the centripetal acceleration of the body is 6 m/s².