Calculate the angular momentum of a solid uniform sphere with a radius of 0.120m and a mass of 14.5kg if it is rotating at 6.15rad/s about an axis through its center.
Part B
Calculate kinetic energy of a solid uniform sphere with a radius of 0.120m and a mass of 14.5kg if it is rotating at 6.15rad/s about an axis through its center.
Part a)
Moment of Ineria for a sphere (formula is different depending on the shape:
I = (2/5)*m*r^2
I = (2/5)*14.5*.120^2 = .0835
Angular momentum = I * angular velocity
.0835 * 6.15 = .51 kgm^2/s
Part B)
Kinetic energy = (1/2)*.0835*(6.15)^2 = 1.579 J
Thanks
To calculate the angular momentum of a rotating object, we use the formula:
L = I * ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
To find the moment of inertia for a solid uniform sphere rotating about an axis through its center, we use the formula:
I = (2/5) * mass * radius^2
Now, let's substitute the given values into the formulas:
Part A:
Mass (m) = 14.5 kg
Radius (r) = 0.120 m
Angular velocity (ω) = 6.15 rad/s
First, let's calculate the moment of inertia using the formula:
I = (2/5) * mass * radius^2
I = (2/5) * 14.5 kg * (0.120 m)^2
Now, we can calculate the angular momentum using the formula:
L = I * ω
L = [(2/5) * 14.5 kg * (0.120 m)^2] * 6.15 rad/s
The angular momentum of the solid uniform sphere is the calculated value from the above equation.
Part B:
To calculate the kinetic energy (KE) of a rotating object, we use the formula:
KE = (1/2) * I * ω^2
Now, let's substitute the given values into the formula:
Mass (m) = 14.5 kg
Radius (r) = 0.120 m
Angular velocity (ω) = 6.15 rad/s
First, let's calculate the moment of inertia using the formula:
I = (2/5) * mass * radius^2
I = (2/5) * 14.5 kg * (0.120 m)^2
Now, we can calculate the kinetic energy using the formula:
KE = (1/2) * I * ω^2
KE = (1/2) * [(2/5) * 14.5 kg * (0.120 m)^2] * (6.15 rad/s)^2
The kinetic energy of the solid uniform sphere is the calculated value from the above equation.