Question

A disc has angular velocity omega about o . The ratio of angular velocity of point p

Answer 1

Answer:

a disc has an angular velocity w about O (centre). the ratio of angular velocity of a point P w.r.t A fixed to the ground and angular velocity of point P w.r.t A fixed to the disc is ? ( P and A are one the circumference of the disc and distance A and P is root 3 R where R is the radius.

Answer 2

The complete question is:

A disc has an angular velocity w about O (center). the ratio of angular velocity of a point P w.r.t A fixed to the ground and angular velocity of point P w.r.t A fixed to the disc is ? ( P and A are one the circumference of the disc) and  the ratio of angular velocity of a point P w.r.t A fixed to the ground and angular velocity of point P w.r.t A fixed to the disc isdistance A and P is root 3 R where R is the radius).

Given:

Angular velocity about center o = w

Distance AP= √3R

To find:

The ratio of angular velocity of a point P w.r.t A fixed to the ground and angular velocity of point P w.r.t A fixed to the disc.

Solution:

Let B be the point on the circle and M be a point that is diametrically opposite to B,

As it is given that AP = √3R

hence, AOM makes an angle of 90° with P

Let α be the angle PAB, then:

cosα = PA/PB = √3R/2R

α = 60°

Let v be the velocity of P with respect to O, then the angular velocity of P with respect to A on the ground is

= vcos30° √3R

And the angular velocity of with respect to moving A on the disc is:

v cos30° √3R / 2v cos30°√3R

= 1/2

The ratio of angular velocity of a point P w.r.t A fixed to the ground and angular velocity of point P w.r.t A fixed to the disc is 1/2.