 If disk angular velocity changes (  is not constant), then we have an angular acceleration   For some point on the disk  From the definition of translational.

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Presentation transcript:

 If disk angular velocity changes (  is not constant), then we have an angular acceleration   For some point on the disk  From the definition of translational acceleration Tangential acceleration (units of m/s 2 )  As the speed changes, this is not Uniform Circular Motion. Also, the Tangential Acceleration is different from the Centripetal Acceleration.

z arar aTaT  Recall  We can find a total resultant acceleration a, since a T and a r are perpendicular   Previously, for the case of uniform circular motion, a T =0 and a=a c =a r. The acceleration vector pointed to the center of the circle.  If a T  0, acceleration points away from the center

Example A thin rigid rod is rotating with a constant angular acceleration about an axis that passes perpendicularly through one of its ends. At one instant, the total acceleration vector (centripetal plus tangential) at the other end of the rod makes a 60.0° angle with respect to the rod and has a magnitude of 15.0 m/s 2. The rod has an angular speed of 2.00 rad/s at this instant. What is the rod’s length? Given: a = 15.0 m/s 2,  = 2.00 rad/s (at some instance)

L x y z  Solve for L

Rolling Motion (Tires, Billiards)  Consider a tire traveling on a road with friction (no skidding) between the tire and road  First, introduce concept of relative velocity. What is the velocity of B as seen by the ground? v axis = v car A C B R=road vTvT vTvT vTvT If tire is suspended, every point on edge has same v T

 Point B has a velocity v T with respect to the A  Now, A (the tire as a whole) is moving to the right with velocity v car  What is velocity of C as seen by the ground?

Example: Problem 8.48 A tire has a radius of m, and its center moves forward with a linear speed of 15.0 m/s. (a) What is  of the wheel? (b) Relative to the axle, what is v T of a point located m from the axle?