I don't understand this: Russian ice skater, Alina Zagitova, spins her way to projected Gold in the 2018 Olympics. During one particular spin, she moves from a camel spin that rotates at about 95. RPM to a

Question

I don't understand this: Russian ice skater, Alina Zagitova, spins her way to projected Gold in the 2018 Olympics. During one particular spin, she moves from a camel spin that rotates at about 95. RPM to a

tight spin. If her rotational inertia changes from 129kgmÂ² to 32kgmÂ², what is the final spin rate of Miss Zagitova in rad/s and RPM?

Where do I insert the factors and into which equations?

Answer 1

Conservation of angular momentum

I1 * omega 1 = I2 * omega2

129 * 95 = 32 * new RPM

by the way

n RPM -> n revs/min * 1 min/60 s * 2 pi rad/rev = n* (2 pi/60) rad/s

Answer 2

To solve this problem, you will need to apply the law of conservation of angular momentum. The angular momentum of an object remains constant unless acted upon by an external torque.

The formula for angular momentum is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

In this case, Alina Zagitova starts with an initial moment of inertia (I1) of 129 kgm² and an initial angular velocity (ω1) of 95 RPM. She then transitions to a final moment of inertia (I2) of 32 kgm².

According to the law of conservation of angular momentum, the initial angular momentum (L1) should be equal to the final angular momentum (L2). Let's write the equation:

L1 = L2

I1ω1 = I2ω2

Now, we can plug in the given values. Remember to convert all units to the correct dimensions:

I1 = 129 kgm²

ω1 = 95 RPM = 95 * (2π/60) rad/s

I2 = 32 kgm²

Let's solve for ω2:

I1ω1 = I2ω2

(129 kgm²) * (95 * (2π/60) rad/s) = (32 kgm²) * ω2

Now, divide both sides of the equation by (32 kgm²) to solve for ω2:

(129 kgm²) * (95 * (2π/60) rad/s) / (32 kgm²) = ω2

Now, calculate the final spin rate in rad/s by evaluating the right side of the equation.

Finally, to convert the final spin rate to RPM, you need to multiply the final spin rate in rad/s by (60/2π) and round the result to the appropriate number of significant figures.

To summarize, you need to insert the given values for I1, ω1, and I2 into the equation I1ω1 = I2ω2 and solve for ω2. Then convert the result to RPM using the conversion factor.