Problem: A wheel that is free to rotate and has a mass of M, a radius of R, and a moment of inertia of I which is centered and is fixed at a point a distance H above the ground. The edge of the wheel is wrapped with a thin thread that is connected to a mass M which is the same as the wheel's mass. When the mass is released from a stationary position, it falls a distance of H in a time period of delta t. In terms of R, M, g, I, and H, what is the duration of this process, delta t? Given: Radius = R Moment of inertia = I Mass = m angular speed = omega_o initial time = 0 coefficient kinetic friction = mu_k velocity center of mass = v_cm Unknowns: Final velocity of the wheel. Final answer should be in variable terms. Target: Determine the wheel's final velocity in terms "I, M, R, and omega o." ( In terms of R, M, g, I, and H, what is the duration of this process, delta t?) Final answer should be in this form: v_f = (equation using I, M, R and omega_o.) (The equations for force, rolling motion, and rotational momentum are all useful when solving the problem. Also please show drawing based on what your solving for. thanks)
Problem:
A wheel that is free to rotate and has a mass of M, a radius of R, and a moment of inertia of I which is centered and is fixed at a point a distance H above the ground. The edge of the wheel is wrapped with a thin thread that is connected to a mass M which is the same as the wheel's mass. When the mass is released from a stationary position, it falls a distance of H in a time period of delta t. In terms of R, M, g, I, and H, what is the duration of this process, delta t?
Given:
Radius = R
Moment of inertia = I
Mass = m
angular speed = omega_o
initial time = 0
coefficient kinetic friction = mu_k
velocity center of mass = v_cm
Unknowns:
Final velocity of the wheel.
Final answer should be in variable terms.
Target:
Determine the wheel's final velocity in terms "I, M, R, and omega o." ( In terms of R, M, g, I, and H, what is the duration of this process, delta t?)
Final answer should be in this form: v_f = (equation using I, M, R and omega_o.)
(The equations for force, rolling motion, and rotational momentum are all useful when solving the problem. Also please show drawing based on what your solving for. thanks)
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