Question

Describe Newton’s 2nd Law of Motion with regards to angular motion. Then compare and contrast your response for angular motion with your response for linear motion.

Answer 1

Newton's 2nd law of motion for Angular motion states that,

If more than one torque acts on a rigid body about a fixed axis, then the sum of the torque equals the moment of inertia times the angular acceleration :

T_i = I .

Compare and Contrast:

Now from Newton's 2nd of motion of Rotation,

= I .---- (1)

where, I = moment of inertia of the body = m r²

Again we know , = r F , where r is the lever arm and F is the force.

putting these values , r F = m r²

or, F = m r ---(2)

We know for linear motion , Newton's 2nd law of motion :

F = m a --(3)

Now compairing equation (2) and (3) we get linear acceleration a = radius r * angular acceleration

and now compairing Newton's 2nd law of motion for Angular motion and for linear motion i.e., equation 1 and 3,

we get, Force ( F ) is equal to Torque ( ) ,

mass ( m ) is equal to Moment of Inertia ( I),

and linear acceleration ( a) is equal to angular acceleration for angular motion.