Rotational Motion Chapter 6, 8 and 9
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
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
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
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
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
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)
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
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
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
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)
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
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