Angular Motion AP Physics 1

Revolving Motion vs Rotating Motion The Earth ____________ around the Sun while _____________ around an axis. Revolving Rotating

What is a rigid body? A rigid body is an object __________________ _____________________________________ _____________________________________. Examples:

3 Motions of a Rigid Body 1.Translational Motion: Examples: 2. Rotational (Angular) Motion: Examples: 3. Combination Motion: Examples:

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……

Example: Convert the following a.60 ⁰ to radiansb. 30 revolutions to radians c rpm to rad/s

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?

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.

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)

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?

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…..

Finding the Center of Gravity