Rotational Motion. Angular Quantities Angular Displacement Angular Speed Angular Acceleration.

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Presentation transcript:

Rotational Motion

Angular Quantities Angular Displacement Angular Speed Angular Acceleration

Linear to Angular Angle to Distance Angular to Linear Velocity Angular to Linear Acceleration r s 

Kinematics For each kinematic equation there is an angular analog.

Bike Ride A bicycle wheel with radius 0.91 m is spinning at 2.2 revolutions per second. If the wheel stops in 50 m, what is the average angular deceleration? 

Torque Torque - Force’s effectiveness in altering rotation motion. (Also called the moment of the force.)  F r Pivot Units (N·m) Torque depends on Distance from pivot Magnitude of applied force Direction of applied force

Diving A 85 kg man stands on a diving board. If he is 2.5 m from the pivot point, what torque is he exerting on the board?

Moment of Inertia From Newton’s 2nd Law Moment of Inertia One particle Multiple particles

Weighted Bar What is the moment of inertia for the object illustrated below if it spins about its center of mass?

Continuous Media For Continuous Media the moment of inertia is Ex. What is the moment of inertia for the washer about its axis if the inner radius is 1.0 cm and the outer radius is 3.0 cm and the mass is 20 g? a b

Atwood’s Machine Two masses are attached to a string and placed over a pulley of mass 2.0 kg and radius 15 cm. What is the acceleration of the masses if m 1 = 3.0 kg and m 2 = 2.0 kg? m1m1 m2m2

Parallel-Axis Theorem If the moment of inertia is know w.r.t. the center of mass, then by shifting the pivot point the new moment of inertia is From the washer in the previous problem what is the moment of inertia about the edge of the washer? h New Pivot CM

Rotational Energy Rotational equivalent to kinetic energy  Pivot

Race Down the Slope A block and a ball move down an inclined plane. The block is able to slide while the ball has enough friction to roll. What are the velocities when they reach the bottom of a 0.25m high slope assuming frictional loses are negligible?