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Homework answers / question archive / 1)Time it takes to complete 5 rotations Distance from the shoulder to the elbow Distance from the shoulder to the middle of the hand Motion of the hand How far in degrees did the hand travel during the five rotations? How far in radians did the hand travel during the five rotations? How far in meters did the hand travel during the five rotations? What was the average angular speed (deg/s and rad/s) of the hand? What was the average linear speed (m/s) of the hand? What was the average angular acceleration (deg/s2 and rad/s2) of the hand? How do you know? What was the average centripetal acceleration (m/s2) of the hand? Motion of the elbow How far in degrees did the elbow travel during the five rotations? How far in radians did the elbow travel during the five rotations? How far in meters did the elbow travel during the five rotations? What was the average angular speed (deg/s and rad/s) of the elbow? What was the average linear speed (m/s) of the elbow? What was the average angular acceleration (deg/s2 and rad/s2) of the elbow? How do you know? What was the average centripetal acceleration (m/s2) of the elbow? Which quantities are different and which quantities are the same for the hand and the elbow? Discuss your answers with your partners and write down questions if you have any

1)Time it takes to complete 5 rotations

- Distance from the shoulder to the elbow
- Distance from the shoulder to the middle of the hand
- Motion of the hand
- How far in degrees did the hand travel during the five rotations?
- How far in radians did the hand travel during the five rotations?
- How far in meters did the hand travel during the five rotations?
- What was the average angular speed (deg/s and rad/s) of the hand?
- What was the average linear speed (m/s) of the hand?
- What was the average angular acceleration (deg/s
^{2}and rad/s^{2}) of the hand? How do you know? - What was the average centripetal acceleration (m/s
^{2}) of the hand?

- Motion of the elbow
- How far in degrees did the elbow travel during the five rotations?
- How far in radians did the elbow travel during the five rotations?
- How far in meters did the elbow travel during the five rotations?
- What was the average angular speed (deg/s and rad/s) of the elbow?
- What was the average linear speed (m/s) of the elbow?
- What was the average angular acceleration (deg/s
^{2}and rad/s^{2}) of the elbow? How do you know? - What was the average centripetal acceleration (m/s
^{2}) of the elbow?

- Which quantities are different and which quantities are the same for the hand and the elbow? Discuss your answers with your partners and write down questions if you have any.

__Exploration:__

- Describe the direction of those arrows, while the angular speed of the wheel is increasing, constant, or decreasing.
- What is the magnitude and direction of the torque on the wheel?
- What happens to the lady bug?
- What provides the centripetal force to keep the bug moving in a circle?
- Why does this eventually fail?
- Observe the acceleration vector after you click Go. How does it change?
- Will the acceleration vector ever point directly to the center? Why or why not?
- What happens to the acceleration vector?
- Use the ruler to measure the radius r of the boundary between the green and pink circles. Record r in your log.
- Calculate what the tangential component of the applied force must have been. Record F
_{tang}in your log. - Compare the torque τ and the angular acceleration α and calculate the moment of inertia I of the disk from τ = Iα. Record I in your log.
- Compare with the moment of inertia displayed in the graph. Record the comparison in your log.
- Set the inner radius equal to 2. Find the moment of inertia for this shape. Record it.
- Even when the force on the platform changes, the moment of inertia graph remains constant. Why?
- While the disk is moving, change the inner radius to 2 m. What happens to the moment of inertia and the angular velocity?
- Make some more changes to the inner radius, outer radius and mass of the disk. Describe what happens.

__Experiment 2:__

- Fill in the table below. Record only magnitudes. (Before taking a force reading, remove the stick, press the tare button, and reattach the stick.)

weight of meter stick and clips |

weight suspended from left clip |

(optional) weight suspended from right clip |

force sensor reading when the stick is again horizontal |

distance d from left clip to force sensor hook (pivot point) |

distance from force sensor hook to CM of meter stick |

distance from force sensor hook to right clip |

- Modeling the meter stick as a forearm and the force sensor as the biceps, compare the force that the biceps has to exert to keep the forearm horizontal to the force it has to exert to just support the weight of the forearm. Comment on the relative magnitude of these forces.
- List all the forces (magnitude and direction) acting on the forearm (meter stick) and calculate all the torques (magnitude and direction) exerted by those forces about the pivot point, when the stick is horizontal and in equilibrium. Do all the forces and torques cancel out?
- Discuss this simple model and your answers with your partners and write down questions if you have any.

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