Astudent sits at rest on a piano stool that can rotate without friction. the moment of inertia of the student-stool system is 4.4 kg⋅m2 . a second student tosses a 2.0 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.45 m from the axis of rotation.

0.56191 rad/s

Explanation:

r = Distance at which the ball is caught = 0.45 m

m = Mass of ball = 2 kg

v = Velocity of ball = 3 m/s

= Moment of inertia of stool student system = 4.4 kgm²

Initial angular momentum is

As the stool rotates the linear momentum is not conserved but the angular momentum is conserved.

Final angular momentum is

Moment of inertia is given by

= Moment of inertia of ball

As the angular momentum of the system is conserved

The angular speed of the stool is 0.56191 rad/s

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.