Help with Physics homework Please and thank you!?

I need help on these two questions. I'm not looking for the answer because I really need to learn how to do this on my own. But if someone could show me what equations to use to answer the steps in the questions and explain to me what each variable in said equations stands for? if you do give an answer please show me how you got it/how to solve it? Thank you

2. A 70.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 10.0 m) and spun at a constant angular velocity of 16.3 rpm. Answer the following:
a. What is the angular velocity of the centrifuge in rad/s?
b. What is the linear velocity of the astronaut at the outer edge of the centrifuge?
c. What is the centripetal acceleration of the astronaut at the end of the centrifuge?
d. How many g’s does the astronaut experience?
e. What is the centripetal force and net torque experienced by the astronaut? Give magnitudes and directions.

3. An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion, as shown in this graph.

Answer the following questions:
a. What is the period and frequency of the pendulum’s motion?
b. How many seconds out of phase with the displacements shown would graphs of the velocity and acceleration be?
c. What is the acceleration due to gravity on the surface of the planet in m/s2? Determine the number of g-forces.

(graph) i.imgur. com /6CouaRj.png

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Sure! Let's go through each question step by step and explain the equations and variables involved.

Question 2:

a. The angular velocity of the centrifuge in rad/s can be obtained by converting the given angular velocity from rpm to rad/s. The conversion factor is given by 2π radians per minute. So, you can use the equation:

Angular velocity in rad/s = (Angular velocity in rpm) * (2π radians/minute)

b. The linear velocity of the astronaut at the outer edge of the centrifuge can be calculated using the formula for linear velocity. The equation is:

Linear velocity = (Angular velocity) * (radius of the centrifuge)

c. The centripetal acceleration of the astronaut at the end of the centrifuge is given by the equation:

Centripetal acceleration = (Linear velocity)^2 / (radius of the centrifuge)

d. To find how many g's the astronaut experiences, we need to compare the centripetal acceleration to the acceleration due to gravity (g). The equation is:

Number of g's = Centripetal acceleration / (acceleration due to gravity)

e. To find the centripetal force and net torque experienced by the astronaut, we need to use Newton's second law and the equations for force and torque. The equations are:

Centripetal force = (mass of the astronaut) * (Centripetal acceleration)
Net torque = (moment of inertia of the astronaut) * (angular acceleration)

Question 3:

a. The period of the pendulum's motion can be calculated using the formula for the period of a pendulum. The equation is:

Period = 2π * √(Length of the pendulum / acceleration due to gravity)

The frequency is the reciprocal of the period.

b. The phase difference between displacements, velocity, and acceleration in simple harmonic motion is π/2 radians or 90 degrees. Therefore, the velocity and acceleration graphs would lag behind the displacement graph by a quarter of the period, or one-fourth of the time for a complete cycle.

c. To find the acceleration due to gravity on the surface of the planet, we need to rearrange the equation for the period of a pendulum and solve for the acceleration due to gravity. The equation is:

Acceleration due to gravity = (4π^2 * Length of the pendulum) / (Period^2)

To determine the number of g-forces, divide the acceleration due to gravity by the acceleration due to gravity on Earth (9.8 m/s^2).

I hope this explanation helps you understand the concepts and equations involved in solving these problems!

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