Miscellaneous Rotation

More interesting relationships

FvP

Pttt

WW

rFW

,

Momentum Formula for Kinetic Energy

m

pK

m

pmK

m

pmmvK

vm

p

mvp

2

2

2

2

21

2

212

21

• Often it is useful to have the formulas for kinetic energy written in terms of momentum.

I

LK

I

LIK

I

LIIK

I

L

IL

2

2

2

2

21

2

212

21

Conservation of Angular MomentumPractice Problem 1

• A disk is rotating with speed wi about a frictionless shaft . Its rotational inertia is I1. It drops onto another disk of rotational inertia I2 that is at rest on the same shaft. Because of friction, the two disks attain a common speed wf. Find wf.

Conservation of Angular MomentumPractice Problem 2

• A merry-go-round (r =2, I = 500 kg m/s2) is rotating about a frictionless pivot, making one revolution every 5 s. A child of mass 25 kg originally standing at the center walks out to the rim. Find the new angular speed of the merry-go-round.

Conservation of Angular MomentumPractice Problem 2

• A merry-go-round (r =2, I = 500 kg m/s2) is rotating about a frictionless pivot, making one revolution every 5 s. A child of mass 25 kg originally standing at the center walks out to the rim. Find the new angular speed of the merry-go-round.

• Ans.- wf=(5/6)wi

Conservation of Angular MomentumPractice Problem 3

• The same child as in the previous problem runs with a speed of 2.5 m/s tangential to the rim of the merry go round, which is initially at rest. Find the final angular velocity of the child and merry go round together.

Conservation of Angular MomentumPractice Problem 3

• The same child as in the previous problem runs with a speed of 2.5 m/s tangential to the rim of the merry go round, which is initially at rest. Find the final angular velocity of the child and merry go round together.

Ans. w= 0.208 rad/s

Conservation of Angular MomentumPractice Problem 4a

• A particle of mass m moves with speed v0 in a circle of radius r0 . The particle is attached to a string that passes through a hole in the table. The string is pulled downward so the mass moves in a circle of radius r. Find the final velocity.

Conservation of Angular MomentumPractice Problem 4a

• A particle of mass m moves with speed v0 in a circle of radius r0 . The particle is attached to a string that passes through a hole in the table. The string is pulled downward so the mass moves in a circle of radius r. Find the final velocity.

Ans. v= (r0/r) v0

Conservation of Angular MomentumPractice Problem 4b

• Find the tension T in the string in terms of m, r, r0 and vo.

3

20

20

r

vmrT

Conservation of Angular MomentumPractice Problem 4b

• Find the tension T in the string in terms of m, r, r0 and vo.

3

20

20

r

vmrT