A child swings a sling with a rock of mass 3.8 kg, in a radius of 0.7. From rest to an angular velocity of 8 rad/s.
What is the rotational kinetic energy of the rock?
Assuming horizontal path of rock.
KE=I w^2=1/2 m(r^2)8^2
To find the rotational kinetic energy of the rock, we can use the formula:
Rotational Kinetic Energy = (1/2) * Moment of Inertia * Angular Velocity^2
To calculate the moment of inertia, we need to know the shape of the rock and its mass distribution. Let's assume it's a solid sphere since you haven't mentioned the specific shape.
The moment of inertia for a solid sphere rotating about its diameter can be calculated using the formula:
Moment of Inertia = (2/5) * mass * radius^2
Given:
Mass of the rock (m) = 3.8 kg
Radius of rotation (r) = 0.7 m
Angular Velocity (ω) = 8 rad/s
1. Calculate the moment of inertia:
Moment of Inertia = (2/5) * mass * radius^2
Moment of Inertia = (2/5) * 3.8 kg * (0.7 m)^2
2. Calculate the rotational kinetic energy:
Rotational Kinetic Energy = (1/2) * Moment of Inertia * Angular Velocity^2
Rotational Kinetic Energy = (1/2) * [(2/5) * 3.8 kg * (0.7 m)^2] * (8 rad/s)^2
Now, you can substitute the known values into the formula and calculate the rotational kinetic energy.