Rotational+Motion

//**Rotational Motion **//

Concept Map

Describing the motion of a rotating body:
How are the linear kinematics quantities related to the angular quantities? How are the linear kinematics equations related to the angular equations?

Definition: an extended body of connected points that are rotating together with the same rotational speed but not necessarily the same linear speed. Example: record player, wheel, figure skater spinning

**Linear Quantities v. Angular (Rotational) Quantities**

Displacement(m) = x vs. Displacement(radians) = Ø

Velocity(m/s) = v vs. Velocity(rad/sec) = omega(w)

Acceleration(m/s²) = a vs. Acceleration(rad/sec²) = alpha

**Linear Motion to Angular Motion Relationships**

x = rØ v = rw a = r(alpha)

 Problem: What is the magnitude of the angular velocity, w, of the second hand of a clock? What is the direction of w as you view a clock hanging vertically? What is the magnitude of the angular acceleration of the second hand?

 Solution: The second hand of a clock goes through an angular displacement of 2p in one minute. Its angular speed is w = 2p/60s = 0.105/s. The direction of w is perpendicular to the face of the clock, pointing into the face of the clock. The average angular acceleration of the second hand is zero.

Linear equations and angular equations are in many ways similar, but replace the linear quantities with angular quantities. Example: V = V(initial) + at... will become ω=ω(initial) + αt

When doing Rotation Motion problems it is important to note that instead of revolutions per unit time you would want the units to become rad per unit time. To make this conversion you will have to keep in mind that: 1 rev = 2π rad

ROTATION IS EASY!!!!! just remember to have your units correct and relate it to linear problems!!!

Practice problem: Levent is riding on a merry-go-round, he wants to go faster than Matt Klein so he sits on the outside of the merry-go-round while forcing Matt into a position closer to the center. The merry-go-round begins and Levent laughs at Matt because Levent thinks that he is going faster, Matt Klein points out that they are going at the same speed. Who is right?????

Answer: They are both right, but in different ways. Levent is faster linearly and Matt is at the same speed as Levent in a rotational sense.