An ice skater is preparing for a jump with turns and has his arms extended. his moment of inertia is 1.7 kg · m2 while his arms are extended, and he is spinning at 0.7 rev/s. if he launches himself into the air at 8.8 m/s at an angle of 45° with respect to the ice, how many revolutions can he execute while airborne if his moment of inertia in the air is 0.7 kg · m2?

2 revolutions.

Explanation:

We need to obtain the angular velocity when he is in the air.

The angular momentum is given by:

Because of angular momentum conservation L1=L2, so the final angular velocity is given by:

We need to calculate the time the skater is in the air, so we need to use the formula of parabolic motion:

so the time taken is 1.26s

the angular displacement is given by:

the number of revolutions is given by:

the skater execute two complete revolutions in the air.

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.