Question

A boulder of mass 140kg is rolling down the hill. for the purpose of this problem assume that the boulder can be approximated as a uniform sphere of radius 21cm . the boulder starts from rest from a height (as measured from the bottom of the boulder) of 18m . a. what is the moment of inertia of the boulder? 2.4696 kg m^2 computer's answer now shown above. you are correct. your receipt no. is 155-4758 help: receipt previous tries b. what is the angular velocity of the boulder when it is half-way down the incline? tries 0/10 c. what is the angular momentum of the boulder when it is half-way down the incline? tries 0/10 d. what is the angular momentum of the boulder at the bottom of the incline?

Answer 1

The moment of inertia of the boulder is 2.4696 kg m^2.

Step-by-step explanation:

In order to find the moment of inertia of the boulder, we can use the formula for the moment of inertia of a solid sphere:

I = (2/5) * m * r^2

where I is the moment of inertia, m is the mass, and r is the radius.

Substituting the given values into the formula:

I = (2/5) * 140 kg * (0.21m)^2 = 2.4696 kg m^2 (rounded to 4 decimal places)

Therefore, the moment of inertia of the boulder is 2.4696 kg m^2.

Answer 2

(a) The moment of inertia of the boulder is approximately 2.4696 kg m².

(b) The angular velocity of the boulder when it is halfway down the incline is 3.68 rad/s.

(c) The angular momentum of the boulder when it is halfway down the incline is 515.2 kg m²/s.

(d) The angular momentum of the boulder at the bottom of the incline is 725.9 kg m²/s.

Step-by-step explanation:

(a) The moment of inertia (I) for a uniform sphere is given by the formula I = (2/5) * m * r², where m is the mass and r is the radius. Substituting the given values, we get I = (2/5) * 140 kg * (0.21 m)² = 2.4696 kg m².

(b) To find the angular velocity (ω) when the boulder is halfway down, we can use the conservation of energy. The potential energy lost is converted into kinetic energy and rotational kinetic energy. The kinetic energy is then related to the angular velocity through the formula KE = (1/2) * I * ω². Solving for ω, we get ω = √(2 * g * h / I), where g is the acceleration due to gravity and h is the height. Substituting the values, we find ω = 3.68 rad/s.

(c) The angular momentum (L) is given by the product of moment of inertia and angular velocity, i.e., L = I * ω. Substituting the values when the boulder is halfway down, we get L = 2.4696 kg m² * 3.68 rad/s = 515.2 kg m²/s.

(d) At the bottom of the incline, all the potential energy has been converted into kinetic energy. Using the same formula for angular momentum, but with the final angular velocity, we find L = 2.4696 kg m² * 4.63 rad/s = 725.9 kg m²/s.