The 5-kg cylinder is initially at rest when it is placed in contact with the wall b and the rotor at a. if the rotor always maintains a constant clockwise angular velocity v = 6 rad> s, determine the initial angular acceleration of the cylinder. the coefficient of kinetic friction at the contacting surfaces b and c is mk = 0.2.

Explanation:

You forgot to include the diagram, but I'm assuming it's the one attached to this answer.

First, sum of the torques equals moment of inertia times angular acceleration.

∑τ = Iα

Fa r - Fb r = (1/2 mr²) α

Fa - Fb = 1/2 m r α

Na μ - Nb μ = 1/2 m r α

μ (Na - Nb) = 1/2 m r α

α = 2μ (Na - Nb) / (m r)

To find the normal forces, we need to take sum of the forces in the x and y directions.

∑Fₓ = maₓ

Nb - Na sin 45 + Fa cos 45 = 0

Nb - Na sin 45 + Na μ cos 45 = 0

Nb - Na (√2 / 2) + Na μ (√2 / 2) = 0

Nb - Na (√2 / 2) (1 + μ) = 0

Nb = Na (√2 / 2) (1 + μ)

∑Fᵧ = maᵧ

Fb - W + Na cos 45 + Fa sin 45 = 0

Nb μ - W + Na cos 45 + Na μ sin 45 = 0

Nb μ - W + Na (√2 / 2) + Na μ (√2 / 2) = 0

Nb μ - W + Na (√2 / 2) (1 + μ) = 0

Substituting:

Nb μ - W + Nb = 0

Nb (μ + 1) = W

Nb = mg / (μ + 1)

Nb = (5 kg) (9.8 m/s²) / (0.2 + 1)

Nb = 40.83 N

Finding Na:

mg / (μ + 1) = Na (√2 / 2) (1 + μ)

Na = mg√2 / (μ + 1)²

Na = (5 kg) (9.8 m/s²) √2 / (0.2 + 1)²

Na = 48.12 N

Therefore:

α = 2μ (Na - Nb) / (m r)

α = 2(0.2) (48.12 - 40.83) / (5 × 0.125)

α = 4.67 rad/s²

Rounding to 1 sig-fig, the angular acceleration is 5 rad/s².

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles