an object of mass 10kg moves in a circle of radius 13m of uniform speed of 43m\s
a) calculate the angular velocity
b) the centripetal force
ANSWER
a) To calculate the angular velocity, we can use the formula:
Angular velocity (ω) = v / r
where v is the linear velocity (speed) and r is the radius of the circle.
In this case, the linear velocity (v) is given as 43 m/s and the radius (r) is given as 13 m.
Using the formula, we can substitute the values:
ω = 43 m/s / 13 m
Calculating this gives us:
ω ≈ 3.31 rad/s
So, the angular velocity of the object is approximately 3.31 rad/s.
b) The centripetal force acting on the object can be calculated using the formula:
Centripetal force (Fc) = mass (m) x (angular velocity (ω))^2 x radius (r)
Given that the mass (m) is 10 kg, the angular velocity (ω) is 3.31 rad/s, and the radius (r) is 13 m, we can substitute these values into the formula:
Fc = 10 kg x (3.31 rad/s)^2 x 13 m
Calculating this gives us:
Fc ≈ 565.39 N
So, the centripetal force acting on the object is approximately 565.39 N.