Review
(a) An object is moving to the left and is slowing down. What is the direction
of its acceleration?
(b) If acceleration is constant, write down one of the kinematics equations
(Chapter 2.)
(c) In 311, you used Newton’s Second Law. Write it in symbols and give the meaning of the symbols in words.
Describing Rotation
1. Here are snapshots of a rotating wheel at 1 second intervals. What
is the appropriate variable with which to describe the rotation? Estimate change
in the angular position from t = 0 seconds to t = 3 s.
How many different (correct) answers can you think of for this estimate?
2.(a)Your group should look at a rotating platform. Start the platform
spinning and record the measurements you make to measure the angular speed of
the platform. Express this angular speed in three units: revolutions/second,
°/sec, and rad/sec.
(b) What additional information must you add to give the angular velocity
rather than the angular speed?
The symbol for angular velocity is the lower case Greek letter omega: 
.
Vector Direction: In addition to clockwise or counterclockwise, we can
give a unique vector direction. The direction of w is along the axis of rotation
(axle) of the rotating object. The axle points both ways so we have a rule to
decide which way is correct. The right-hand rule for angular velocity (Hitchhiker’s
rule): Wrap the fingers of your right hand around a pencil with the thumb along
the pencil. Orient your hand so the fingers curl around the object in the direction
it rotates. The thumb gives the vector direction of angular velocity.
Angular acceleration, Greek lower-case alpha: 
.
3. Below are three sketches of angle versus time. Sketch the corresponding
graphs of angular velocity and angular acceleration versus time. Each group
member should do a different column.
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4. Consider the following demonstration: a bicycle wheel has a
hub around which a string is wrapped. The other end of the string is connected
to a mass. The wheel is given an initial spin so that the mass begins
to rise. The coordinate system has right = +x, up (toward top of paper)
= +y, and out-of-the-paper = +z.
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(d) Is the angular acceleration CW or CCW? What is its vector direction?
(e) Your friend stands on the other side of the wheel from you, but uses the
same coordinate system. How would his answers differ from yours for the four
parts above?
Relation between Angular and Linear quantities.
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A wheel of radius R has a string wrapped around the rim and connected to a mass. The string does not slip or stretch. When the wheel rotates through an angle theta, by how much does the mass rise? How do radians help you solve this problem?
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What is the name of the path traveled by a point at the rim of the wheel?
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Sketch of the angular position of a point at the rim of the wheel as a function of time. |
| theta | | | | _|__________________________ | | time |
When a rigid wheel rotates, any point on the wheel has a velocity that is tangent
to the wheel, vt. What is the relation between the angular velocity
and the tangential velocity?
Velocity is a vector. Acceleration measures the rate of change of the
velocity vector with time. Can the magnitude of a velocity change without a
change in direction? Yes No
(Circle one.)
Explain.
Can the direction of a velocity change without a change in magnitude? Yes
No (Circle one.)
Explain.
What is the relation between the angular acceleration and the tangential acceleration?
What is the relation between the angular velocity and the radial (centripetal) acceleration?
Examples:
1. A wheel rotates initially 0.25 rev/sec clockwise. After 1.5 sec it
has rotated to an angle 65² clockwise relative to the initial orientation. Find
the angular acceleration.
| 2. A wheel is shown with a hub of radius 2.0 cm and an outer radius
of 5.0 cm. String wrapped around the hub is connected to mass m1 and string
wrapped around the wheel is attached to mass m2. Initially mass m1 is moving
downwards at 15 cm/s, but it is momentarily at rest after moving 25 cm down.
(a) What is the acceleration of mass m1? (b) What is the initial angular velocity, including direction? (c) What is the initial radial (centripetal) acceleration of a point at the edge of the wheel? (d) What is the angular acceleration of the wheel, including direction? (e) What is the initial velocity of mass m2, the striped mass, including direction? |
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(f) Through what angle does the wheel rotate before momentarily stopping?
(g) How far does m2, the striped mass, rise before momentarily stopping?
This page maintained by Anne G. Young. Last modified 08-Mar-2004 .