Question

Problem 1: Gymnastics Bars A gymnast jumping onto a bar can swing herself around it at high speed. Assume she is 160 cm tall, and that she has the moment of inertia of a thin rod. A. The center of gravity of her torso (with mass 35 kg) is a distance of 50 cm from the top of her head, and the center of gravity for her legs (with mass 23 kg) is at a distance of 110 cm from the top of her head. How far is her center of gravity from the top of her head? B. If she jumps onto a gymnastics bar with her body at an angle of 25° below the horizontal, as shown above, draw an extended free body diagram clearly indicating the pivot (i.e. the axis of rotation). C. What is the net torque on the gymnast about the pivot you indicated? Her head is 40 cm from the bar. D. Using the result of C, find her angular acceleration (for the moment of inertia, you may model her as a thin rod rotating about its end). E. How do the following quantities change, as she rotates around the bar? Explain your reasoning for each case. 1. The net torque on her body. 2. Her angular acceleration. 3. Her angular velocity. F. If the maximum linear velocity her center of mass reaches is 2.3 m/s, what is her maximum angular velocity?

          Problem 1: Gymnastics Bars
A gymnast jumping onto a bar can swing herself
around it at high speed. Assume she is 160 cm tall,
and that she has the moment of inertia of a thin
rod.
A. The center of gravity of her torso (with
mass 35 kg) is a distance of 50 cm from
the top of her head, and the center of
gravity for her legs (with mass 23 kg) is at
a distance of 110 cm from the top of her
head. How far is her center of gravity from the top of her head?
B. If she jumps onto a gymnastics bar with her body at an angle of 25° below the horizontal,
as shown above, draw an extended free body diagram clearly indicating the pivot (i.e. the
axis of rotation).
C. What is the net torque on the gymnast about the pivot you indicated? Her head is 40 cm
from the bar.
D. Using the result of C, find her angular acceleration (for the moment of inertia, you may
model her as a thin rod rotating about its end).
E. How do the following quantities change, as she rotates around the bar? Explain your
reasoning for each case.
1. The net torque on her body.
2. Her angular acceleration.
3. Her angular velocity.
F. If the maximum linear velocity her center of mass reaches is 2.3 m/s, what is her
maximum angular velocity?

Problem 1: Gymnastics Bars
A gymnast jumping onto a bar can swing herself
around it at high speed. Assume she is 160 cm tall,
and that she has the moment of inertia of a thin
rod.
A. The center of gravity of her torso (with
mass 35 kg) is a distance of 50 cm from
the top of her head, and the center of
gravity for her legs (with mass 23 kg) is at
a distance of 110 cm from the top of her
head. How far is her center of gravity from the top of her head?
B. If she jumps onto a gymnastics bar with her body at an angle of 25° below the horizontal,
as shown above, draw an extended free body diagram clearly indicating the pivot (i.e. the
axis of rotation).
C. What is the net torque on the gymnast about the pivot you indicated? Her head is 40 cm
from the bar.
D. Using the result of C, find her angular acceleration (for the moment of inertia, you may
model her as a thin rod rotating about its end).
E. How do the following quantities change, as she rotates around the bar? Explain your
reasoning for each case.
1. The net torque on her body.
2. Her angular acceleration.
3. Her angular velocity.
F. If the maximum linear velocity her center of mass reaches is 2.3 m/s, what is her
maximum angular velocity?

Added by Amy P.

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