Module H
Torque and Motion Relationships

Page 318: Questions # 1, 2, 3, 5 [answers in bold print]

1.    What distinguishes angular velocity from speed?  Give an example for each.

Angular velocity specifies the direction of rotation as well as the magnitude (speed) of rotation.  Angular velocity: A somersaulting diver rotates 360 degrees per second in a clockwise direction.  Angular speed: A diver rotates 360 degrees per second.

2.    If a body is rotating with constant angular velocity, what is its aceleration?

If angular velocity is constant (no change in speed or direction), its angular acceleration is zero.

3.    Which segment has the gratest angular acceleration: (a) an arm that gains an angular velocity of 300 degrees per second in .5 sec, or (b) an arm that gains an angular velocity of 200 degrees per second in .2 sec?

Angular acceleration = change in angular velocity divided by time.  The arm in b has greater angular acceleration (200/.2 = 1000 deg/sec/sec) than the arm in a (300/.5 = 600deg/sec/sec)

5.    What is the instnataneous release velocity of a softball released by an upper extremity, .5m long, that is rotating at 573 degrees per second at the time of release?  (remember to use radians in v=rw)

The instantaneous release velocity is calculated by v = rw
v = .5m x 573 deg/sec x 1rad/57.3deg
   = .4m x 10 rad/ sec
   = 5m/sec

Note that radians are not part of the units for linear velocity.

------------------------------------------------------------------------------------------------------------------------

Pages 324-325: Questions # 1, 2, 4, 7 [answers in bold print]

1.    Describe the difference between the mass (inertia) of your arm and its rotational inertia.

The inertia of your arm is its resistance to a change in its linear motion and is measured by your arm's mass.  The rotational inertia of your arm is its resistance to a change in its state of angular motion and is measured by its mass and also how far away that mass is distributed from its axis of rotation.

2.    Grip a baseball bat and rotate it back and forth horizontally.  Grip it at the oposite end and rotate it as before.  Compare the difficulty with which the same mass may be rotated depending on how the mass is destributed from the axis of rotation.  Explain.

The bat may be rotated (angularly accelerated and decelerated) back and forth more easily when it is gripped near its more massive end.  The mass of the bat does not change; however, the bat may be swung more easily when its mass is distributed closer to its axis of rotation near the wrist joints because it rotational inertia is minimal.

4.    Hold your arms horizontally out to your sides and rapidly swing them up and down in a vertical plane several times.  Next, bend the elbows to place your fingers at the front of your shoulder joints.  Repeat the sweeping motion of the arms in a vertical plane.  Explain the difference in difficulty (you ahve not altered the mass of the arm).

It should be more difficult to swing the arms in the longer position because their masses are distributed as far away from the shoulder joint axis as possible, thereby maximizing their rotational inertias.

7.    Examine the masses and shapes or mass distribution of the following body segments and make a conclusion regarding the amount of muscle torque necessary to rotate these segments: (a) upper arm, (b) forearm, (c) hand, (d) fingers,
(e) thigh, (f) lower leg, (g) foot.

Examination of these body segments will lead to the conclusion that they are of decreasing mass as they are farther away from the center of the body (the more distal segments are less massive).  Also, the shapes of the segments of the limbs are such that the more massive regions tend to be close to their proximal axes of rotation, thereby tending to decrease their resistance to rotation.