11/7 Rotational Energy Today: Rotational Energy Examples HW: 11/6 HW Handout “Rotational Energy” due Wednesday 11/13 Exam 3: Thursday, 11/14 Monday holiday-no lab next week!

Rotational Kinetic Energy Just another bucket KER KE = 1/2mv2 Ring has same m and same v so KER,Ring = KET,Block Disk has same m but mass near center is slower so less KER here KER,Disk = 1/2KET,Block Ring of mass m rotating with velocity v Disk of mass m rotating with velocity v Block of mass m moving with velocity v

Proportional Reasoning Rolling without slipping means that vR = vT Find total KE of ring and disk KET = 24J KET = 24J KET = 24J KER = 24J KER = 12J Total KE = 24J Total KE = 48J Total KE = 36J

Proportional Reasoning Rolling without slipping means that vR = vT Now all have Total KE = 72J. Find the velocity if the mass is 2kg. KET = 72J KET = 36J KET = 48J (2/3 of total) KER = 36J KER = 24J (1/3 of total) Total KE = 72J Total KE = 72J v = 8.5m/s Total KE = 72J v = 6m/s v = 6.9m/s

Use Energy to fins the velocity of the ring. R T g S 1/2PEg = KET h R T g S 1/2mgh = 1/2mv2 vT vT = gh Rolls without slipping so vR = vT and KER = KET since it is a ring. Use Energy to fins the velocity of the ring.

For the disk R T g S R T g S 2/3PEg = KET h 2/3mgh = 1/2mv2 3 v = 4gh R T g S R T g S 2/3PEg = KET h 2/3mgh = 1/2mv2 3 v = 4gh Rolls without slipping so vR = vT and KER = 1/2KET since it is a disk.

Systems of objects A Skateboard made of 4 wheels (disks, 1kg each) and a board (2kg). Rolls without slipping at 1m/s So 1/4 in rotation and 3/4 in translation Sort the total energy into buckets: KET = Board and Wheels = 3J KER = Just Wheels KER of disk = 1/2 KET of disk KET of disk = 0.5J so KER disk = 0.25J KER = 1J for all 4 wheels