If the sphere on the left is moved closer to the central cylinder and placed at a distance r/2 from the axis of rotation, what is the magnitude of the angular acceleration α of the modified system? assume that the rest of the system doesn't change.

Explanation:

The torque reqired to rotate the above masses rod system

...............(1)

Total moment of inertia of masses and rod is

=

now Substitute I= in the (1) we get

rearranging for alpha we get

hence the acceleration is

a electromagnetic waves

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.