At a certain time, a 55-kg person is 25 m due north of you and is walking at a speed of 1.2 m/s exactly southwest. What are the magnitude and direction of this person’s angular momentum about you?
To find the magnitude and direction of a person's angular momentum, we need to consider both their linear momentum and their distance from the point of reference, in this case, you.
Angular momentum is given by the formula:
L = mvr sinθ
Where:
L is the angular momentum,
m is the mass of the object (in this case, the person),
v is the linear velocity of the object,
r is the distance of the object from the reference point, and
θ is the angle between the linear velocity vector and the position vector.
Let's break down the given information:
- The mass of the person is 55 kg (m = 55 kg).
- The person is walking at a speed of 1.2 m/s (v = 1.2 m/s).
- The person is 25 m due north of you (r = 25 m).
To calculate the angle θ, we need to consider the directions. The person is moving southwest, which we can break down into a combination of south and west directions.
The angle between the linear velocity and position vector is given by:
θ = atan(y/x)
Where:
x is the horizontal distance between the person and you (west direction).
y is the vertical distance between the person and you (south direction).
We can calculate x and y using trigonometry:
x = cos(45°) * 25 m
y = sin(45°) * 25 m
Now, we can calculate θ:
θ = atan(y/x)
Lastly, we can calculate the magnitude of angular momentum:
L = mvr sinθ
And the direction of angular momentum will be the same as the direction of the angular velocity vector, which is perpendicular to both the velocity and the position vectors.
By carrying out these calculations, we can determine the magnitude and direction of the person's angular momentum about you.