Question

a 7.00 kg mass and a 4.00 kg mass are mounted on a spindle that is free to turn about the x axis as shown. Assume the mass of the arms as shown. Assume the mass of the arms and the spindle to be negligible. the gravitational acerlation is 9.81 m/s^s and the lever length is r2=3m then r1=5m*cos37

Answer 1

The angular acceleration of the pulley is approximately 3.75 rad/s².

Step-by-step explanation:

The angular acceleration of the pulley can be calculated using the formula:

a = Στ / I

where τ is the torque and I is the moment of inertia. Given that the radius of the pulley is 20 cm and the mass of the weights are 1.0 kg and 2.0 kg respectively, we can calculate the torques:

τ₁ = r₁F₁ = 0.20 m × 1.0 kg × 9.81 m/s² = 1.962 N·m

τ₂ = r₂F₂ = 0.20 m × 2.0 kg × 9.81 m/s² = 3.924 N·m

Substituting the values into the formula, we get:

a = (Στ) / I = (τ₁ + τ₂) / (m₁r₁² + m₂r₂²) = (1.962 N·m + 3.924 N·m) / (1.0 kg × (0.20 m)² + 2.0 kg × (0.20 m)²)

Solving the equation, we find that the angular acceleration of the pulley is approximately 3.75 rad/s².