118 Rotational Energy

1
11/8 Rotational Energy

• Today Rotational Energy Examples
• HW 11/8 HW Handout Skateboard due Thursday
  11/14
  
• Exam 3 Thursday, 11/145-7 in 116, 6-8 in 114,
  Email me if other time needed
  
• Monday holiday-no lab next week!

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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
Total Energy 4J
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
3
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
How fast would the skateboard be moving if it
rolled from rest without slipping down a ramp,
losing 4m of altitude?
Energy still split 1/4 3/4
0
0
0
0
0
KER 60J
Top of ramp
Bottom of ramp
KET 180J
PE 240J
1/2mv2 180J
v 7.75m/s
4
Pulley and Block
We have a block with mass 3m hanging from a ring
(pulley) of mass m and radius r, which rides on a
frictionless axle. The system is released from
rest.
Axle
Energy of the system
m
0
0
0
PE is for the block only.
top
Where is the energy?How is it split?
0
bottom
1/4 3/4 3 parts T and 1 part R
3m
v 0
How do the velocities of the block and ring
compare?
How do the velocities of the block and string
compare?
h
vB vString vR not slipping!
v ?
How do the masses of the block and ring compare?
How does the KER of the ring compare to the KET
of the block?
5
Pulley and Block
We have a block with mass 3m hanging from a ring
(pulley) of mass m and radius r, which rides on a
frictionless axle. The system is released from
rest.
Axle
m
PE is for the block only.
Where is the energy?How is it split?
0
0
1/4 3/4
3/4mgh 1/2mv2
3m
v 0
h
v ?