What is the angular momentum of a 0.200- ball rotating on the end of a thin string in a circle of radius 1.45 at an angular speed of 13.0 ?
Angular momentum is L = I•ω,
where I = m•R² is the moment of inertia of the material point.
L = I•ω = m•R²• ω =
=0.2 (kg)•(1.45)² (m²) •13 (rad/s) =
=5.47 kg•m²/s.
Well, I bet that ball is really dizzy spinning around like that! But don't worry, I'll calculate its angular momentum for you.
Angular momentum is given by the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular speed.
To find the moment of inertia (I) for a sphere rotating around an axis that passes through its center, we use the formula I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius.
Since the ball has a mass of 0.200 kg and is rotating at a radius of 1.45 m, we can plug these values into the formula to find the moment of inertia:
I = (2/5) * 0.200 kg * (1.45 m)^2
Now, we can calculate the angular momentum:
L = I * ω
So, just plug in the values and calculate. And remember, while you're doing this, make sure you don't get yourself in a spin!
To calculate the angular momentum of a rotating object, we can use the formula:
Angular momentum (L) = moment of inertia (I) * angular speed (ω)
The moment of inertia for a point mass rotating around an axis at a distance r can be calculated using the formula:
Moment of inertia (I) = mass (m) * radius squared (r^2)
Given:
Mass (m) = 0.200 kg
Radius (r) = 1.45 m
Angular speed (ω) = 13.0 rad/s
First, let's calculate the moment of inertia (I) using the given mass and radius:
I = m * r^2
I = 0.200 kg * (1.45 m)^2
Next, let's substitute the values into the formula for angular momentum:
L = I * ω
L = (0.200 kg * (1.45 m)^2) * 13.0 rad/s
Now, let's calculate the angular momentum:
L = (0.200 kg * 2.1025 m^2) * 13.0 rad/s
L = 0.4205 kg.m^2 * 13.0 rad/s
L ≈ 5.4665 kg.m^2/s
Therefore, the angular momentum of the 0.200 kg ball rotating on the end of a thin string in a circle of radius 1.45 m at an angular speed of 13.0 rad/s is approximately 5.4665 kg.m^2/s.
To calculate the angular momentum of a rotating object, you need to know its moment of inertia and angular velocity.
The moment of inertia for a point mass revolving around an axis at a distance 'r' is given by the formula: I = m * r^2, where 'm' is the mass of the object and 'r' is the distance from the axis of rotation to the mass.
In this case, the ball has a mass of 0.200 kg, and it is rotating at a radius of 1.45 m. So, the moment of inertia can be calculated as follows: I = 0.200 kg * (1.45 m)^2.
The angular velocity of the ball is given as 13.0 rad/s.
The formula for angular momentum is L = I * ω, where 'L' is angular momentum, 'I' is moment of inertia, and 'ω' is angular velocity.
By substituting the values into the formula, you can calculate the angular momentum:
L = (0.200 kg * (1.45 m)^2) * 13.0 rad/s
Now, you can evaluate this expression to find the angular momentum of the ball on the end of the string.