1. Rotational Motion Chapter 6, 8 and 9

2. Acceleration in a Circle  Acceleration occurs when velocity changes  This means either speed OR direction changes  So objects moving in a circle are accelerating even if speed remains constant because they are constantly changing direction

3. Centripetal Acceleration  In order to accelerate, there must be a net force in the direction of acceleration according to Newton’s 2 nd Law  This means there must be a center- directed force  This is called centripetal force  Without centripetal force, inertia would cause the object to continue in a straight line at a constant speed

4. Centrifugal Force  When moving quickly in a circle, you feel like you are being pushed outward  This is called centrifugal force  The is no outward force, only a inward force (centripetal force)  Centrifugal force is an imaginary force because it doesn’t have a reaction force to accompany it  You feel the outward force because inertia wants you to keep moving in a straight line, but the centripetal force forces you to move in a circle instead

5. Angular velocity (ω)  A measure of what angle an object is able to travel per unit time  Unit is rad/s  All parts of a rigid body rotate with the same ω, that means object’s near the edge have to cover more distance in the same amount of time (have a higher tangential velocity)  Angular measures differ from centripetal measures because the object is rotating around it’s center of mass instead of orbiting an outside point

6. Angular Acceleration (α)  A measure of how quickly angular velocity is changing  Unit is rad/s 2  Again, this differs from centripetal acceleration because it is rotation of an object around its center of mass as opposed to revolving around an external point

7. Starting Rotation  Caused by torque (τ) acting on an object  This is rotational force  Unit is a Nm  Two parts to torque:  Lever arm  To get the most effect, effort force should be exerted as far from the axis of rotation as possible (why doorknobs are at the edge of a door)  L = r, if the force is exerted perpendicular to the axis of rotation  Force  Often the weight of an object (Fw = mg)

8. Net Torque  If clockwise torque = counterclockwise torque, then net torque is zero and no rotation occurs  This is called static equilibrium or translational equilibrium  There is no velocity or acceleration

9. Moment of Inertia (I)  Not only mass matters for rotation, its location also matters  The further from the axis a mass is, the harder it is to turn  This is why you choke up on a baseball bat to make it easier to swing  Can change this by changing the mass or where the mass is located in relationship to the axis of rotation

10. Newton’s 2nd Law Modified  Normally, acceleration is equal to force divided by mass  In rotational motion, force is replaced by torque and mass is replaced by moment of inertia  The same equation, with distance from axis of rotation added to account for circular motion

11. Center of Mass (COM)  Each object has a center of mass (COM)  This COM follows all motion laws, the rest of the object rotates around this point  To find COM, suspend the object at 2 different points. Draw a vertical line down the object from that point. Where the two lines cross is the COM  This is typically higher on a male’s body then a female’s  You can change your COM by changing your shape  COM can be located in empty space (ex. donut)

12. Toppling  Objects topple when their COM is no longer over its support base (τ net no longer = 0)  Considered stable if an external force is needed to cause toppling  The lower the COM, the more stable the object

13. Angular Momentum (L)  Like linear momentum, but with all our modified angular measures  Is the product of momentum of inertia and angular velocity  The product of torque and time is the angular impulse which causes a change in angular momentum  It’s still conserved, like linear momentum  So, if your decrease your radius (and therefore your I), your angular velocity must increase  This is why you spin faster when you pull in your arms when ice skating