A child swings a sling with a rock of mass 1.3 kg, in a radius of 0.6. From rest to an angular velocity of 6 rad/s. What is the rotational kinetic energy of the rock?

8.42Joules

Explanation:

The rotational kinetic energy, denoted by E(rotational), can be calculated using the formula:

E(rotational) = 1/2 × I × ω²

Where;

I = moment of inertia (kgm²)

ω = angular velocity (rad/s)

However, we need to calculate the moment of inertia in this question by using the formula:

I = m × r²

Where;

m = mass (1.3kg)

r = radius (0.6m)

I = 1.3 × 0.6²

I = 1.3 × 0.36

I = 0.468 kgm²

Since I = 0.468 kgm², ω = 6 rad/s, we can calculate rational kinetic energy using:

K.E(rotational) = 1/2 × I × ω²

K.E(rotational) = 1/2 × 0.468 × 6²

K.E(rotational) =1/2 × 0.468 × 36

K.E(rotational) = 18 × 0.468

K.E(rotational) = 8.424

K.E(rotational) = 8.42Joules

their crystal patterns have been disrupted by stress

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west