A cricket bowler bowls a cricket ball witha mass of 150g and a radius of 52mm. The bowler's arm weighs 3.4kg and has a length of 0.68m. The centre of mass of the bowler's arm act's at it's midpoint. What is the moment of inertia of the cricket ball and bowler's arm?
To calculate the moment of inertia of the cricket ball and bowler's arm, we need to consider the individual contributions of each object separately and then add them up.
1. Moment of Inertia of the Cricket Ball:
The moment of inertia for a solid sphere about its center is given by the formula:
I = (2/5) * m * r^2
where I is the moment of inertia, m is the mass of the object, and r is the radius.
Given:
Mass of the cricket ball (m) = 150g = 0.15kg
Radius of the cricket ball (r) = 52mm = 0.052m
Plugging the values into the formula, we get:
I_cricket ball = (2/5) * 0.15 * (0.052)^2
= 0.0008088 kg.m^2
2. Moment of Inertia of the Bowler's Arm:
The moment of inertia for a rod about its center is given by the formula:
I = (1/12) * m * L^2
where I is the moment of inertia, m is the mass of the object, and L is the length of the object.
Given:
Mass of the bowler's arm (m) = 3.4kg
Length of the bowler's arm (L) = 0.68m
Plugging the values into the formula, we get:
I_bowler's arm = (1/12) * 3.4 * (0.68)^2
= 0.05462 kg.m^2
3. Total Moment of Inertia:
To find the total moment of inertia, we simply add the moment of inertia of the cricket ball and the bowler's arm:
I_total = I_cricket ball + I_bowler's arm
= 0.0008088 + 0.05462
= 0.0554288 kg.m^2
Therefore, the moment of inertia of the cricket ball and bowler's arm combined is approximately 0.0554288 kg.m^2.