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Chapter_10

# Chapter_10 - Reminders Graded make-up exam 2 can be viewed...

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Reminders Graded make-up exam 2 can be viewed after class or during office hours, and requests for regrading must be submitted by Wed 3/24 . Quiz scores are available on UBlearns.

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Chapter 10 Rotation In this chapter we will study the rotational motion of rigid bodies about a fixed axis. We will introduce the following new concepts (analogous to old concepts in translational motion): - Angular displacement -Average and instantaneous angular velocity (symbol: ω ) -Average and instantaneous angular acceleration (symbol: α ) -Rotational inertia also known as moment of inertia (symbol I ) - Torque (symbol τ ) We will also calculate the kinetic energy associated with rotation, write Newton’s second law for rotational motion, and introduce the work-kinetic energy theorem for rotational motion (10-1)
The Rotational Variables We will study the rotational motion of rigid bodies about fixed axes . A rigid body is defined as one that can rotate with all its parts locked together. A fixed axis means that the object rotates about an axis that does not move. We can describe the motion of a rigid body rotating about a fixed axis by specifying just one parameter . We take the the z -axis to be the fixed axis of rotation. We define a reference line which is fixed in the rigid body and is perpendicular to the rotational axis. From top view, the angular position of the reference line at any time t is defined by the angle θ(t) that the reference line makes with the position at t = 0. θ(t) defines the position of all the points on the rigid body because all the points are locked as they rotate. The angle θ is related to the arc length s traveled by a point at a distance r from the axis via the equation Note: The angle θ is measured in radians s r θ= (10-2)

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t 1 t 2 1 2 1 2 2 1 We show the reference line at a time and at a later time . Between and the body undergoes an . All the points of the rigid body have the = - Angular Displacement angular displacement t t t t θ angular displacement because they are locked together. same ( 29 2 1 1 2 1 2 We define for the time interval , : The SI unit for angular velocity is ra We de dians/s fine th e n e d l co - = = = - Angular Velocity avg t t t t t ϖ average angular velocity instantaneous angular velocity 0 im = . If a rigid body rotates counterclockwise (CCW) has a positive sign. If the rotation is clockwise (CW) has a negative s ign ∆ → Algebraic sign of angular velocity : t d t dt (10-3) d dt ϖ= dx v dt =
If the angular velocity of a rotating rigid object changes with time, we can describe how fast changes by defining the Angular Acceleration angular aceleration ϖ (10-4) ω 1 ω 2 t 1 t 2 d dt α= dv a dt = ( 29 1 2 1 2 2 1 1 1 1 2 2 2 In the figure we show the reference line at time and . The angular velocity is at and at .

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Chapter_10 - Reminders Graded make-up exam 2 can be viewed...

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