Question

2. An iceskater is turning at a PERIOD of (1/3) second with his arms outstretched. a) What is his ANGULAR VELOCITY w? b) If he pulls his arms towards his body to reduce his MOMENT OF INTERTIA by 1⁄2, what is his ANGULAR VELOCITY w? c) How much does his ROTATIONAL KINETIC ENERGY change? That is, if the initial Kinetic Energy is (KE)initial, what is the final KE? d) Where did that ENERGY come from, or go to?

Answer #1

A figure skater is spinning slowly with arms outstretched. He
brings his arms in close to his body and his angular velocity
changes by a factor of 2. By what factor does his moment of inertia
change, and why?

The outstretched hands and arms of a figure skater preparing for
a spin can be considered a slender rod pivoting about an axis
through its center (Figure 1). When his hands and arms are brought
in and wrapped around his body to execute the spin, the hands and
arms can be considered a thin-walled hollow cylinder. His hands and
arms have a combined mass 9.0 kg . When outstretched, they span 1.6
m ; when wrapped, they form a cylinder...

The outstretched hands and arms of a figure skater preparing for
a spin can be considered a slender rod pivoting about an axis
through its center (Figure 1). When his hands and arms are brought
in and wrapped around his body to execute the spin, the hands and
arms can be considered a thin-walled hollow cylinder. His hands and
arms have a combined mass 8.0 kg . When outstretched, they span 1.7
m ; when wrapped, they form a thin-walled...

The outstretched hands and arms of a figure skater preparing for
a spin can be considered a slender rod pivoting about an axis
through its center. (See the figure below (Figure 1).) When the
skater's hands and arms are brought in and wrapped around his body
to execute the spin, the hands and arms can be considered a
thin-walled hollow cylinder. His hands and arms have a combined
mass of 7.5 kgkg . When outstretched, they span 1.8 mm ;...

In this example we see how a system can have constant angular
momentum without having a constant angular velocity! A physics
professor stands at the center of a turntable, holding his arms
extended horizontally, with a 5.0 kg dumbbell in each hand (Figure
1). He is set rotating about a vertical axis, making one revolution
in 2.0 s. His moment of inertia (without the dumbbells) is 3.4
kg⋅m2 when his arms are outstretched, and drops to 1.8 kg⋅m2 when
his...

In this example we see how a system can have constant angular
momentum without having a constant angular velocity! A physics
professor stands at the center of a turntable, holding his arms
extended horizontally, with a 5.0 kgkg dumbbell in each hand
(Figure 1). He is set rotating about a vertical axis, making one
revolution in 2.0 ss. His moment of inertia (without the dumbbells)
is 3.4 kg⋅m2kg⋅m2 when his arms are outstretched, and drops to 1.8
kg⋅m2kg⋅m2 when his...

A physics teacher does a classroom demonstration on a rotating
table illustrating angular momentum. His body has a moment of
inertia of 6.21 kg-m^2. He puts a one kilogram mass in each hand
and with his arms outstretched, he begins spinning at 27 rpm. The
masses are initially at 54 cm from the axis of rotation. He then
pulls his arms into his body and the masses end up at a radius of 8
cm from the axis of rotation....

An ice skater spins about a vertical axis with an angular speed
of 15 rad/s with arms fully extended horizontally. Then the arms
are pulled in quickly with no friction. Suppose the initial
rotational inertia is 1.72 kg*m^2 and the final is .61 kg*m^2.
a) what is the final angular velocity of the skater?
b) what is the change in the skater's kinetic energy?
c) where does the additional kinetic engery come from? What is
being done when the arms...

Suppose a 0.250 kg ball is thrown at 13.0 m/s to a motionless
person standing on ice who catches it with an outstretched arm as
shown in Figure 9.31.
(a) Calculate the final linear velocity of the person, given his
mass is 80.0 kg.
(b) What is his angular velocity if each arm has a 5.00 kg mass?
You may treat his arms as uniform rods of length 0.9 m and the rest
of his body as a uniform cylinder...

Suppose a 0.250 kg ball is thrown at 13.0 m/s to a motionless
person standing on ice who catches it with an outstretched arm as
shown in Figure 9.31.
Figure 9.31.
(a) Calculate the final linear velocity of the person, given his
mass is 76.0 kg: This is the answer: .043 m/s (I know
this).
(b) What is his angular velocity if each arm has a 5.00
kg mass? You may treat his arms as uniform rods of length 0.9...

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