Question

Suppose the particles in the preceding problem have masses m1=0.10kg,m2=0.20kg,m3=0.30kg, m4=0.40kg. The velocities of the particles are v1=2.0ˆim/s, v2=(3.0ˆi−3.0ˆj)m/s, v3=−1.5ˆjm/s, v4=−4.0ˆim/s. (a) Calculate the angular momentum of each particle about the origin.

a) 0.20kg⋅m^2/s
b) 0.40kg⋅m^2/s
c) −0.30kg⋅m^2/s
d) 0.80kg⋅m^2/s

Answer 1

The angular momentum of each particle is calculated using the formula: Angular Momentum = mass * velocity * distance. For particle 1, the angular momentum is 0.40 kg·m²/s. For particle 2, the angular momentum is 1.20 kg·m²/s. For particle 3, the angular momentum is -0.67 kg·m²/s. For particle 4, the angular momentum is -6.40 kg·m²/s.

Step-by-step explanation:

To calculate the angular momentum of each particle, we use the formula:

Angular Momentum = mass * velocity * distance

For particle 1: Angular Momentum = 0.10 kg * 2.0 î m/s * 2.0 m = 0.40 kg·m²/s

For particle 2: Angular Momentum = 0.20 kg * (3.0 î - 3.0 ĵ) m/s * √(3.0² + (-3.0)²) m = 1.20 kg·m²/s

For particle 3: Angular Momentum = 0.30 kg * (-1.5 ĵ) m/s * 1.5 m = -0.67 kg·m²/s

For particle 4: Angular Momentum = 0.40 kg * (-4.0 î) m/s * 4.0 m = -6.40 kg·m²/s