A diver curls up when he performs a stunt. Explain. Calculate the angular momentum of a body rotating with 20rpm and M.I 4kg m²
When a diver performs a stunt and curls up, it is done to change their body's rotational inertia. The rotational inertia, also known as the moment of inertia, determines how difficult it is to change the angular motion of an object. By curling up, the diver is effectively reducing their body's moment of inertia, making it easier to rotate.
To calculate the angular momentum of a body rotating at a given angular speed (in this case, 20 rpm) and with a given moment of inertia (4 kg m²), we can use the following formula:
Angular momentum (L) = Moment of inertia (I) x Angular velocity (ω)
Angular velocity (ω) is given in radians per second. To convert from rpm (revolutions per minute) to radians per second, we need to multiply by 2π/60, as there are 2π radians in a full revolution and 60 seconds in a minute.
Therefore, the angular velocity is calculated as:
ω = (20 rpm) x (2π rad/1 rev) x (1 rev/60 s) = 20 x 2π/60 rad/s ≈ 2.094 rad/s
Now, we can substitute the values into the formula to calculate angular momentum:
L = (4 kg m²) x (2.094 rad/s) = 8.376 kg m²/s
So, the angular momentum of the rotating body is approximately 8.376 kg m²/s.