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Rotation & Torque

Rotation & Torque. AP Physics. Rotation: Position & Velocity. The angle “ θ ” used to represent rotational position Units: radians or degrees (remember 2 π rad = 360 o ) Change in rotational position during some time interval is average angular velocity , ω . θ 2. ω. Δ θ. θ 1. ω.

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Rotation & Torque

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  1. Rotation & Torque AP Physics

  2. Rotation: Position & Velocity The angle “θ” used to represent rotational position • Units: radians or degrees (remember 2πrad = 360o) Change in rotational position during some time interval is average angular velocity, ω. θ2 ω Δθ θ1 ω

  3. Rotation: Acceleration Change in angular velocity during some time interval is average angular acceleration, α.

  4. Rotation of a Compact Disc A compact disc (CD) rotates at high speed while a laser reads data encoded in a spiral pattern. The disc has a radius r = 6 cm. At some point while the data is being “read” from the disc, it spins at 7200 rpm. • What is the CD’s angular velocity in radians per second? • How much time is required for it to rotate through 90o? • If it starts from rest and reaches full speed in 4.0 s, what is its average angular acceleration?

  5. Comparison of Linear and Angular Motion If the angular acceleration is constant the same constant acceleration equations learned previously apply to a rotating body. *s is the arc length of a circle *r is the radius of the circle s θ2 Δθ θ1 r ω

  6. …Torque The quantitative measure of the tendency of a force to cause or change rotational motion around an axis. Torque is the product of the magnitude of the force and the moment arm (the perpendicular distance between the axis and the force). Door (top view) Axis of rotation r θ F

  7. Amateur Plumber Luigi, the amateur plumber, is unable to loosen a pipe fitting. He decides to slip a piece of scrap pipe (a “cheater”) over the handle of his wrench. He then applies his full weight of 900 N to the end of the cheater by standing on it. The distance from the center of the fitting to the point where the weight acts is 0.80 m, and the wrench handle and cheater make an angle of 19o with the horizontal. Find the magnitude and direction of the torque of his weight about the center of the pipe fitting.

  8. Equilibrium Translational Equilibrium The net forces acting on an object are equal to zero. ∑ F = 0 Object is in translational equilibrium when it’s not accelerating. Rotational Equilibrium The net torques acting on an object are equal to zero. ∑ τ= 0 Object is in rotational equilibrium when the angular acceleration is zero. Static Equilibrium There must be both Translational Equilibrium and Rotational Equilibrium. The sum of the torques and the sum of the forces must both add to zero.

  9. Recess: The Seesaw A uniform 40 N board supports two children weighing 500 N and 350 N. The support (often called the fulcrum) is under the center of the board, and the 500 N child is 1.5 m from the center. How far from the center of the board will the 350 N child be for the seesaw to be at rotational equilibrium? 1.5 m x = ? F = 350 N Fulcrum F = 500 N

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