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Rotational Motion

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.

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Rotational Motion

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  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 2nd 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/s2 • 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

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