Atypical pencil has an average length of 15.0 cm and an average mass of 10.0 g. assume the tip of the pencil does not slip as it falls.
1. what is the angular acceleration of the pencil when it makes an angle of 10.0 degrees with the vertical? express your answer numerically in radians per second squared to three significant figures.

α = 17.0 rad/s²

Explanation:

For this problem let's use the torque expression

         τ = I α

Torque is the product of force by the distance that is half the length of the pencil

        τ = F x

Let's use trigonometry

        sin 10 = x / (l / 2)

        x = l / 2 sin 10

        τ = mg l /2  sin 10

The moment of inertia of pencil that we approximate as a rod with the axis of rotation at one end

          I = 1/3 m L²

 We replace

          mg l / 2 sin 10 = 1/3 m l² α

           α = 3/2 g/l  sin 10  

Let's reduce the magnitudes to the SI system

            l = 15.0 cm = 0.150 m

           m = 10.0 g = 0.0100 kg

Let's calculate

            α = 3/2 9.8 / 0.150 sin 10

            α = 17.0 rad/s²

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

pretty sure it's false