Question

A particle accelerates uniformly from rest at 0.15π rad/s2 from rest. The particle’s initial position is at 45° from the negative x – axis. If the particle moves a distance 15m along the arc of radius 2m for a time of 1.15 seconds, determine (a) position of the particle after 1.15 seconds from the +x – axis, (b) the initial and final angular velocity, (c) the tangential velocity and acceleration of the particle at 2 seconds?

Answer 1

Solution of (a):

We have,
Angular acceleration
Arc length
Radius
Time duration

The initial position of the particle is from the negative x-axis, therefore, initial position of the particle from the positive x-axis is given as:

The initial angular velocity of the particle is because particle started its motion from rest.

The final position of the particle can be calculated from the kinematics formula:

Solution of (b):

The initial angular velocity of the particle is because particle started its motion from rest.

The final angular velocity of the particle after   is calculated from the kinematics formula:

The final angular velocity of the particle will be .

Solution of (c):

Since angular acceleration of the particle is uniform, its tangential acceleration will also be uniform, there tangential acceleration of the particle is given after time is:

The tangential velocity of the particle after time is calculated from the linear kinematics formula:

Where is the initial tangential velocity of the particle which is because particle started from the rest.

Therefore, the tangential velocity of the particle after time is .