Question

Typed please. An ice skater can change the speed of her rotation by bringing her arms close to her body. Because her angular momentum is approximately conserved, why does she rotate faster? Before she starts spinning, how does she generate rotation in the first place?

Answer #1

As per the conservation of angular momentum,

The product of initial moment of inertia and initial angular velocity is always equal to the product of final moment of inertia and final angular velocity.

Mathematically,

I1 w1 = I2 w2

When an ice skater brings are closer to the body its moment of inertia decreases and hence the angular velocity w2 increases so as to keep the angular momentum constant.

Before she start spinning she generates rotation in the first place by applying the tangential force which results into a net torque, thus giving rotational kinetic energy

A rapidly spinning ice skater has her hands close to her body.
She then extends her arms horizontally. What change, if any, will
there be in the following quantities related to her motion?
Moment of Inertia, Angular velocity, Angular Momentum.
Ignoring friction, tell whether each would increase,
decrease, or remain constant.

a figure skater presses off the ice to begin spinning with her
arms close to her body. after completing 2 turns in 0.8 seconds she
moves her arms further away from her body, what will her new
angular velocity be?
a. <16.6rad/s
b. 18 rad/s
c. 20 rad/s
d. 24 rad/s

A skater is spinning on the ice and extends her arms out
straight. Discuss the effect this will have on her moment of
inertia, her angular momentum, and her angular velocity. Will each
increase, decrease, or stay the same? Explain. Please be
specific?

What is the angular momentum of a figure skater spinning at
3.2rev/s with arms in close to her body, assuming her to be a
uniform cylinder with a height of 1.5m , a radius of 16cm , and a
mass of 55kg?
How much torque is required to slow her to a stop in 4.4s ,
assuming she does not move her arms?

When a figure skater goes into spin she will begin with her arms
extended, and then draws her arms inward. As a result the ice
skater spins faster. Describe why this works in terms of angular
momentum.
Provide your own example of the conservation of linear momentum
in a collision. Use the words elastic, inelastic, and totally
inelastic in your explanation.

What is the angular momentum of a figure skater spinning at 2.3
rev/s with arms in close to her body, assuming her to be a uniform
cylinder with a height of 1.5 m, a radius of 16 cm , and a mass of
49 kg ?
How much torque(in magnitude) is required to slow her to a stop
in 4.8 s , assuming she does not move her arms?

a. What is the angular momentum of a figure skater spinning at
2.0 rev/s with arms in close to her body, assuming her to be a
uniform cylinder with a height of 1 m, a radius of 0.2 m, and a
mass of 50 kg?
b. How much torque is required to slow her to a stop in 5.0 s,
assuming she does not move her arms?

Diana, a figure skater, is initially spinning at an angular
speed 2.50 rev/s, with her arms and legs inward. Assume that she is
a uniform cylinder with a height of 1.4 m, a radius of 18 cm, and a
mass of 55 kg. Assume no external torques act.
a) What is her moment of inertia?
b) If she extends her arms outward, what is her new moment of
inertia? Assume that
her armspan is 1.3 m and her arms are...

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?

Explain how a figure skater uses the concept of angular momentum to
control her angular speed , when she is spinning.

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