A student sits on a rotating stool holding two 2.6 kg masses. When his arms are extended horizontally, the masses are 0.71 m from the axis of rotation, and he rotates with an angular velocity of 1.8 rad/sec. The student then pulls the weights horizontally to a shorter distance 0.23 m from the rotation axis and his angular velocity increases to ω2. For simplicity, assume the student himself plus the stool he sits on have constant combined moment of inertia Is = 3.8 kg m2 . Find the new angular velocity ω2 of the student after he has pulled in the weights. Answer in units of rad/s.

2.8 rad/s

Explanation:

In absence of external forces, the total angular momentum of the system must be conserved.

The angular momentum when the arms of the student are extended horizontally is given by:

where:

is the moment of inertia of the student+stool

is the moment of inertia of each mass, where:

m = 2.6 kg is one mass

r = 0.71 m is the distance of each mass from the rotation axis

is the initial angular velocity

So we have

When the student pulls the weights to a distance of r' = 0.23 m, the angular momentum is:

where:

is the new moment of inertia of each mass, with

r' = 0.23 m

Since the angular momentum must be constant, we have:

and solving for , we find the final angular velocity:

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.