Questions dealing with Angular momentum (but maybe kinetic engery)

[Prodan]

I recently had a question on a test that just boggled my mind. I could not find the answer and unfortunatley could not consult a T.A. I have a vague memory of the question. It is a figure skater rotating at angular velocity w = 2 rad/s (not sure if that number is correct). The figure skater is holding a sphere mass 150grams(.15kg) which is located .6 meters from the axis of rotation. The sphere is 1.6m from the ground.
a) What is the net force acting on the small sphere? (I said gravity but was not sure)
b) How long will it take the ball to hit the ground if released?
c) Calculate the Initial Kinetic Energy given the final Kinetic engery is 12000 J. (I think this was the phrasing of last question)

At first I thought of using the
mgh + 1/2I(Inertia)w(Angular vel)^2 = 1/2mv^2(1+ I(Intertia of Centre of Mass) / MR^2)

We are not given intertia though? or did i remember this incorrectly perhaps? Would it make more sense to have intertia?

I am truley stumped, any help would be awesome.

Kevin

 

[blochwave]

a)Well it's rotating. If the only force acting on it was gravity, it wouldn't be rotating. In fact, there's also a normal force on it from her hands since she hasn't dropped it yet, so it's just the centripetal force

b)The rotational motion has no effect on it falling, it's just your typical falling object problem

c)Remember the final kinetic energy is only translational, once she let's go the centripetal force goes away and it's only traveling linearly(EDIT: In the sense that it's not going to be KEtotal=1/2mv^2+1/2Iw^2, just 1/2mv^2, and it'll travel in a parabolic arc like you always see with projectile motion)

Also the moment of inertia of a point mass is just mr^2, where r is its distance from the rotational axis. You should assume it's a point mass, a solid sphere has a different moment of inertia but you're not given a radius of the sphere, so I don't think you assume that

 

[Moetasim]

I can provide some guidance on how to approach this question. First, let's clarify some concepts. Angular momentum is a measure of an object's rotational motion, while kinetic energy is a measure of an object's motion in a straight line. In this case, the figure skater is rotating at a constant angular velocity of 2 rad/s, which means that the speed of the skater's rotation remains constant. This angular velocity can be calculated using the formula w = v/r, where v is the tangential velocity and r is the radius of rotation (in this case, the distance from the axis of rotation to the center of the sphere).

Now, let's address the questions one by one:

a) The net force acting on the small sphere is gravity, as you correctly stated. This is because the only external force acting on the sphere is the force of gravity pulling it towards the ground. The formula for the force of gravity is F = mg, where m is the mass of the object (0.15 kg) and g is the acceleration due to gravity (9.8 m/s^2).

b) To calculate the time it takes for the ball to hit the ground, we can use the equation d = 1/2gt^2, where d is the distance the ball falls (1.6 m) and g is the acceleration due to gravity. Rearranging the equation, we get t = √(2d/g) = √(2*1.6/9.8) ≈ 0.57 seconds.

c) To calculate the initial kinetic energy, we can use the formula KE = 1/2mv^2, where m is the mass of the object (0.15 kg) and v is the velocity of the object. In this case, we are given the final kinetic energy (KE = 12000 J) and we can solve for v using the formula v = √(2KE/m). Plugging in the values, we get v = √(2*12000/0.15) ≈ 346.4 m/s. This is the velocity at which the ball would hit the ground if it was released from the skater's hand.

I hope this helps clarify the concepts and equations involved in this question. Remember to always carefully read and understand the question, and to use the appropriate formulas and units when solving problems involving angular momentum and kinetic