# Torque and angular momentum

• killerinstinct
In summary, a bee of mass M alights (lands softly) on a thin horizontal rod of mass 3M and length l which pivots frictionlessly about its center. The bee exerts a torque of 4g on the rod, which causes it to rotate about its center at a maximum angular velocity of 360 degrees per second.f

#### killerinstinct

1. a bee of mass M alights (lands softly) on a thin horizontal rod of mass 3M and length l which pivots frictionlessly about its center.

a) what torque did it exert
b) angular acceleration of rod when bee lands.
c) maximum angular velocity when bee reaches LOWEST point?

try:
a) torque = r x F = lmg
b) torque = I a
lmg = a 1/12 (3m) l squared
a = 4g / l
c) use kinematics??

2. atwood machine with frictionless 1.00 kg wheel and radium 0.1 is suspended with two masses on a massless rope. mass A is 2.0 kg. B is 1.5 kg.
a) Relate torque to net force on each of the two masses b) acceleration? c) tensions on THREE?? ropes?

attempt:
a) torque = r x F. but what is r?
b) i know how to do it for massless wheel. but how to incorporate a massed wheel?
c) don't understand the question.

3. A cylinder of mass M and R SLIDES with initial velocity of V0 down an inclinded plane with angle theta. mu is kinetic friction. a) what is acceleration of the objects Center of MASS B) torque on cylinder C) acceleration of cylinder? d) what speed will the object stop sliding and starts to roll?

attempt:
torque = mu m g R = I a
wR= v, for rolling
sigma = w/2 t

1. a bee of mass M alights (lands softly) on a thin horizontal rod of mass 3M and length l which pivots frictionlessly about its center.

a) what torque did it exert
b) angular acceleration of rod when bee lands.
c) maximum angular velocity when bee reaches LOWEST point?

try:
a) torque = r x F = lmg
b) torque = I a
lmg = a 1/12 (3m) l squared
a = 4g / l
c) use kinematics??
a) Where does the bee land? How far from the center?
c) Since the acceleration is not constant as the stick pivots, using kinematics will be too hard. Hint: Is anything conserved?

2. atwood machine with frictionless 1.00 kg wheel and radium 0.1 is suspended with two masses on a massless rope. mass A is 2.0 kg. B is 1.5 kg.
a) Relate torque to net force on each of the two masses b) acceleration? c) tensions on THREE?? ropes?

attempt:
a) torque = r x F. but what is r?
b) i know how to do it for massless wheel. but how to incorporate a massed wheel?
c) don't understand the question.
a) You are given the radius.
b) You need to analyze forces on the two masses and the wheel. Combine those three equations to solve for the acceleration.
c) The atwood machine is suspended from a rope (assume it's attached to the ceiling); that's the third rope.

3. A cylinder of mass M and R SLIDES with initial velocity of V0 down an inclinded plane with angle theta. mu is kinetic friction. a) what is acceleration of the objects Center of MASS B) torque on cylinder C) acceleration of cylinder? d) what speed will the object stop sliding and starts to roll?

attempt:
torque = mu m g R = I a
wR= v, for rolling
sigma = w/2 t
a) What forces act on the cylinder?
b) What torque do those forces exert?
c) The cylinder's center slows down, while it's rotation speeds up. At some point, the condition for rolling without slipping will be met--find that point.

1a) lands at end of the rod.
1c) conservation of mechanical energy??
4mgh = 1/2 I w squared??
can you type that out LaTeX for me?

2) torque = rF
Force of tension - m1g = m1a1 = -m1a
Ft-M2g=m2a2 = m2a
force on wheel (i'm stuck here)
2c) do this problem as a system??

3) gravity acts on the cylinder.
ah... i still don't understand the physics part of this...
I'd like to see the process (steps in solving this). i think that would help.
can i see the latex for this and i will expain it back to you to show you that i understand.