 # Rotational Motion Angular Quantities Angular Displacement Angular Speed

• Slides: 14 Rotational Motion Angular Quantities • Angular Displacement • Angular Speed • Angular Acceleration Linear to Angular • Angle to Distance • Angular to Linear Velocity • Angular to Linear Acceleration q 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? w Torque • Torque - Force’s effectiveness in altering rotation motion. (Also called the moment of the force. ) F Pivot Torque depends on Distance from pivot Magnitude of applied force Direction of applied force q r Units (N·m) 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 2 nd 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? b a 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? m 2 m 1 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? New Pivot h CM Rotational Energy • Rotational equivalent to kinetic energy w 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. 25 m high slope assuming frictional loses are negligible?