Question

show work please

Robert has a forearm length of 0.35m. And a radius of gyration about the center of mass of 42% his forearm length from the elbow. The following information are provided to you: Total body mass: 68 Kg Forearm mass: 1.6 % of total body mass Center of mass location: 39% of forearm length from the elbow

5. Given this radius of gyration, what is his forearm’s moment of inertia about the center of mass? A. 0.024 Kgm2 B. 0.020 Kgm2 C. 0.045 Kgm2 D. 0.029 Kgm2

6. What is forearm’s moment of inertia about the elbow? A. 0.024 Kgm2 B. 0.020 Kgm2 C. 0.045 Kgm2 D. 0.029 Kgm2

7. During a dive, why does the diver go into tuck position in the flight phase? A. To increase angular momentum B. To decrease angular momentum C. To increase angular velocity D. To increase moment of inertia

8. During a dive, why does the diver straighten out his/her body right before he/she is about to enter the water? A. To increase angular momentum B. To decrease angular momentum C. To increase moment of inertia D. To increase angular velocity

Answer 1

* Radius of gyration is defined as the distance from the axis of rotation to a point where the total mass of the body is supposed to be concentrated i.e. centre mass, so that the moment of inertia about the axis may remain the same.

The basic principle involved is law of conservation of angular mmentum.

   L =Iw

If  L is constant then

I w = constant

Whenever moment of inertia decreses , angular speed increases and vice-versa inorder to conserve angular momentum.

5) Forearm’s moment of inertia about the center of mass

Total body mass = 68 Kg

forearm length = 0.35m

Forearm mass m = 1.6% of total body mass = (1.6/100)x68 = 1.088 kg = 1.1 kg

   Radius of gyration k = 42% of forearm length from the elbow = ( 42 / 100 ) x 0.35 = 0.147 m

Forearm’s moment of inertia about the center of mass = I = m k² = 1.1 x (0.147)² = 0.024 kg m²

(A)  0.024 kg m²

6) Forearm’s moment of inertia about the elbow

   Forearm mass m = 1.6% of total body mass = (1.6/100)x68 = 1.088 kg = 1.1 kg

   Radius of gyration k = 39% of forearm length from the elbow = ( 39 / 100 ) x 0.35 = 0.1365 m

Forearm’s moment of inertia about the center of mass = I = m k² = 1.1 x (0.1365)² = 0.020 kg m²

(B)  0.020 kg m²

7)   During a dive, why does the diver go into tuck position in the flight phase?

Inoder to conserve angular momemtum ,   the diver go into tuck position in the flight phase during a dive.

The basic principle involved is law of conservation of angular mmentum.

L = I w

where L is angular momentum , w is angular speed and I is moment o inertia

  

twinkl.com

The above diagram depicts tuck position.

* If the diver goes into tuck position

i)   radius of gyration (k) decreases then moment of inertia decreases

I = m k²

I directly proportional to k²

Therefore

as moment of inertia decreases , inorder to conserve the momentum angular velocity should increase.

L =Iw

If  L is constant then

I w = constant

Whenever moment of inertia decreses , angular velocity increases and vice-vrsa inorder to conserve angular momentum.

Where w is angular speed and I is moment of inertia.

(C)   To increase angular velocity

8)  During a dive, why does the diver straighten out his/her body right before he/she is about to enter the water?

whenever the diver straighten out his/her body right before he/she is about to enter the water

i ) Radius of gyration increases and  moment of inertia increase   

I = m k²

I directly proportional to k²

Therefore

as moment of inertia increases , inorder to conserve the momentum angular speed should decrease.

L =I w

If  L is constant then

I w = constant

Whenever the moment of inertia Increases , angular speed decreases and vice-versa inorder to conserve angular momentum .

Where w is angular speed and I is moment of inertia.

(C). To increase moment of inertia