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Angular Motion AP Physics 1
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Revolving Motion vs Rotating Motion The Earth ____________ around the Sun while _____________ around an axis. Revolving Rotating
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What is a rigid body? A rigid body is an object __________________ _____________________________________ _____________________________________. Examples:
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3 Motions of a Rigid Body 1.Translational Motion: Examples: 2. Rotational (Angular) Motion: Examples: 3. Combination Motion: Examples:
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Translational Motion to Angular Motion Translational Motion VariableAngular Motion Variable ∆ x (m) Ѳ (rads) v (m/s)ω (rad/s) a (m/s 2 )α (rad/s 2 ) v = ωr Speed of a point on the rigid body a = αr Acceleration of a point on the rigid body Let’s take a look at our reference pack……
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Example: Convert the following a.60 ⁰ to radiansb. 30 revolutions to radians c. 1500 rpm to rad/s
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Example: A tire with a diameter of 90 cm starts from rest and makes 15 revolutions in 5 s. a.What is the angular acceleration of the tire? b.What is the angular velocity of the tire at the end of the 5 seconds? c.What is the translational acceleration of a point on the outside edge of the tire? d.What is the translational velocity of a point on halfway to the outside edge of the tire? How would that velocity compare to the velocity of a point on the outside edge of the tire?
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Torque, (τ) analogous to force in that force produces linear acceleration and torque produces rotational, or angular acceleration Line of action – extended line collinear with the force Lever arm – distance l between the line of action and the axis of rotation, measured on the line perpendicular to both.
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The “sin θ” term comes from the fact that only forces tangential to the circle (of radius r centered on the axis of rotation) cause torque: Thus, radial forces do not cause torque. Direction: the torque is positive if the force tends to produce a counterclockwise rotation about the axis, and negative if the force tends to produce a clockwise rotation. Units: mN (meter -Newton)
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Example: Two forces act on a wheel, as shown below. The wheel is free to rotate without friction, has a radius of 0.42 m, and is initially at rest. Given that F 1 = 12 N and F 2 = 9.5 N, find (a) the torque caused by F 1 and (b) the torque caused by F 2. (c) In which direction does the wheel turn as a result of these two forces?
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Gravitational Torque and the Center of Gravity We won’t prove it but…….. The weight of an object acts at a single special point on the object called its ____________________________. Facts about the center of gravity of an object: Images of center of gravity…..
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Finding the Center of Gravity
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