Question of Physics

Question

A particle of mass m is moving in a circular path of radius R. The angular speed of the particle is given by ω = βt^3/2. Find the tangential and the radial (centripetal) forces acting on the particle as a function of time t. θ and r are the tangential and radial unit vectors. Is the motion uniform or non-uniform? Explain your answer briefly.

Answer 1

TANGENTIAL FORCE:

Let F be the tangential force (to be found),

I = mR² be the moment of inertia of the particle

α = dω/dt = (3/2)βt^1/2 be the angular acceleration.

We compute F from the relationship among the above three quantities:

RF = Iα = mR²(3/2)βt^1/2

F = (3β/2)mRt^1/2

CENTRIPETAL FORCE:

It is given by formula

mω²R = mRβ²t³

The motion is not uniform because "uniform circular motion" is defined as one

with constant angular velocity.