Question

Physics Ques! Rotational Kinetic Energy problem I am having.

I need a sample problem pertaining to rotational KE that uses spherical rotation. Please use either of the two diagrams in my picture to create a problem.

Make sure the following equation is used to solve the problem.

PE=(KE)₁(KE)₂ + 1/2mv²

Also I need to solve for velocity of the object on the string, of mass 'm'.

Here is the picture with the diagrams of the two problems I need an example for one of or both of, whichever:

There are more equations in the picture that I need to use, especially :

mgh = 1/2 I w² + 1/2 mv²

In the case of the final problem's diagram.

Any amounts for variables are fine, whatever example problem of how rotational KE works in this way is perfect.

Thanks very much!

EDIT: There are no known values as I am asking for someone to please show an example of this type of problem.

This is just a problem to show how rotational Kinetic Energy,etc works.

Known values can be whatever works for the equation. But for the unknown values I need an example of Solving for velocity of the mass on the string please.

But the unknown value I need an example of Solving for velocity of the mass on the string please.

Please help! Thank you! My test is tomorrow!!

Answer 1

Conservation of energy T_r 4 E_i + R 4 E_i + GPE_i = Y_ 4E_s + RRE_f + G PE_f rightdoublearrow 1/2 MV^2_0 + 1/2 IW^2_0 = Mg H rightdoublearrow V^2_0/2 [M + I/R^2] = Mg H rightdoublearrow H = V^2_0/2g [1 + I/MR^2] (10) Change in Translate energy = 1/2 mv^2_0 - 0 = 1/2 MV^2_0 (11) W_surrounding + W_g = 4E_s - 4E_i W_syrr + (0 - Mg H] = 1/2 M 0 - [1/2 MV^2_0 + 1/2 Iw^2_0] rightdoublearrow W_surrounding = 0 (12) Change in angular momentum = L_i - L_f = [MV_0 R + I V_)/R = MV_0R [1 + I/MR^2]