A small mass M attached to a string slides in a circle (x) on a frictionless hor

Question

A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y).

true false greater than less than equal to  M's angular momentum at y is .... that at x.
true false greater than less than equal to  As M moves from x to y, the work done by F is .... 0.
true false greater than less than equal to  M's kinetic energy at y is four times that at x.
true false greater than less than equal to  While going from x to y, there is no torque on M.
true false greater than less than equal to  M's angular velocity at x is one quarter that at y.

Explanation / Answer

The force causing an object to travel in a circle is called centripetal force
Centripetal force = mass * velocity^2 ÷ radius

Eq. #1 Fx = mass * vx^2 ÷ r1
Eq. #2 Fy = mass * vy^2 ÷ (½ * r1)

Divide Eq #2 by Eq. #1
vy^2 / vx^2 = ½

KE = ½ * mass * velocity^2
Ke y/KE x = ½

1) M's kinetic energy at y is four times that at x. False , KE at y is 2 times KE at x

Angular momentum = moment of inertia * angular velocity
Moment of inertia = mass * radius^2
Angular velocity = radians/ sec
Angular momentum = mass * radius^2 *

The radius at x is 2 times radius at y.
The angular velocity at x is ½ the angular at y.
Angular momentum at x = mass * (2 * ry)^2 * ½ * y
Angular momentum at y = mass * ry^2 * y

Angular momentum at x/angular momentum at y
= mass * (2 * ry)^2 * ½ * y / mass * ry^2 * y = r

2) Angular momentum at x / angular momentum at y = 4/2 = 2

M's angular momentum at x is greater than that at y.
M’a angular momentum at x is 2 times angular momentum at y

3) As M moves from x to y, the work done by F is greater than 0.

Work = increase in Kinetic energy, so work is +, greater than 0

4) M's angular velocity at y is twice that at x. False, angular velocity at y is twice that at x

5) While going from x to y, there is a torque on M TRUE

because the tension in the string is causing the mass to rotate around the center of the circle

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