Question

A diver goes into a somersault during a dive by tucking her limbs. If her rotational kinetic energy is 100 J and her moment of inertia in the tuck is 9.0 kg·m^2, what is her rotational rate during the somersault?

a) 3.0 rad/s
b) 4.0 rad/s
c) 5.0 rad/s
d) 6.0 rad/s

Answer 1

By rearranging the formula for rotational kinetic energy to solve for angular velocity and using the given values, the rotational rate of the diver during her somersault is approximately 5.0 rad/s (option c).

Step-by-step explanation:

To calculate the rotational rate of the diver during her somersault, we can use the relationship between rotational kinetic energy (KErot) and the moment of inertia (I) and angular velocity (ω). The formula for rotational kinetic energy is:

KErot = (1/2) · I · ω2

Given that the diver's rotational kinetic energy is 100 J and her moment of inertia is 9.0 kg·m2, we can rearrange the formula to solve for ω (rotational rate):

ω = √(2 · KErot / I)

ω = √(2 · 100 J / 9.0 kg·m2)

ω = √(200 / 9.0)

ω = √(22.22)

ω = 4.7 rad/s (approximately)

However, since this is not one of the offered options, we must round to the nearest choice, which is 5.0 rad/s (option c).