What is the angular momentum (in kilogram-meter^2/second) of a 500.0 g ball rotating on the end of a string in a circle of radius 1.54 m at an angular speed of 2.50 rad/s?
500 * 1.54 = x
500 * x * 2.50^2
thank you,
but since it has to be in kg, do i do the same thing but with
0.5*1.54=0.77
0.5*0.77*2.50^2 = 2.406 kgm^2/s
To find the angular momentum of the rotating ball, we can use the formula:
Angular Momentum = Moment of inertia * Angular Speed
First, we need to find the moment of inertia of the ball. The moment of inertia depends on the mass distribution and the axis of rotation. For a point particle rotating about an axis perpendicular to it, the moment of inertia is given by:
Moment of Inertia = mass * radius^2
Given:
Mass of the ball (m) = 500.0 g = 0.5 kg
Radius (r) = 1.54 m
Using these values, we can calculate the moment of inertia:
Moment of Inertia = 0.5 kg * (1.54 m)^2
Next, we need to find the angular speed (ω). The angular speed is given as 2.50 rad/s.
Now, we can substitute the values into the angular momentum formula:
Angular Momentum = Moment of Inertia * Angular Speed
Angular Momentum = (0.5 kg * (1.54 m)^2) * 2.50 rad/s
To find the units of the angular momentum, we multiply the units of moment of inertia (kg-m^2) by the units of angular speed (1/s):
Angular Momentum = (0.5 kg * (1.54 m)^2) * (2.50 rad/s)
Angular Momentum = kg-m^2/s
Therefore, the angular momentum of the ball rotating on the end of a string is given as kg-m^2/s.