Physics 3 – Sept 5, 2017 P3 Challenge – A hoop and a disk of identical mass and radius are rolled up two identical inclined planes without slipping and reach a maximum height of Hhoop and Hdisk respectively before coming momentarily to rest and rolling back down. Use one of the three signs <, > or = in the boxes below to correctly complete each statement. 1) If both hoop and disk start with the same total kinetic energy then: Hhoop Hdisk 2) If both hoop and disk start with the same center of mass speed then:
Objectives/Agenda/Assignment B.1 Work, Power and Angular momentum (1.9 – 1.10) Agenda: Work and Power Angular Momentum Assignment: Read/reread p1-15. Do p16 #14-17
Work and Power For work and power the analogy of variables continues: Linear motion Rotational motion F = ma Γ = Iα W = F Δs W = Γ Δθ P = Fv P = Γω The work kinetic energy theorem also holds: W = ½ Iω2 - ½ Iω2
Rotational Work Problem How much work is done on a ship’s wheel by a sailor if a constant 45.0 N force is applied while the wheel is turned 30 from rest? Let the radius of the wheel be 58.0 cm. If this is the only force present, how fast would the wheel be spinning after the sailor lets go? Let the rotational inertia of the wheel be 6.50 kg m2.
Angular momentum Angular momentum completes the analogy. Linear momentum p = mv Angular momentum L = Iω Conservation of angular momentum is the third great conservation of motion kind of laws. (The other two being conservation of energy and conservation of momentum.) As a result of conservation of angular momentum, objects when have a change in their moment of inertia will spin either slower (increase in I – more mass far away from axis of rotation) or faster (decrease in I – more mass close to the axis of rotation.)
Angular momentum problem Predict the angular speed of Earth if it became a black hole. Assume the earth is a solid homogenous sphere. M = 5.981024 kg and R = 6.37 106 m and it would have a radius of 8.86 mm as a black hole.
Exit slip and homework Exit Slip – A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm, rotational inertia 5.0 x10-3 kg m2, and frictionless bearings. The cockroach’s speed (relative to the ground) is 2.0 m/s, and the lazy Susan turns clockwise with angular speed v0= 2.8 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. What is the angular speed of the lazy Susan after the cockroach stops? What’s due? (homework for a homework check next class) Read/reread p1-15.Do p16 14-17 What’s next? (What to read to prepare for the next class) Review for rotation test next Tuesday, Sept 12