Question

A disc has a diameter of one meter and rotates about an axis passing through its center and at right angles to its plane at the rate of 120 rev/min. Calculate the angular and linear velocities of a point on the rim and at a point halfway to the center?

Answer 1

Given: A disc has a diameter of one meter and rotates about an axis passing through its center and at right angles to its plane at the rate of 120 rev/min.

To find the angular and linear velocities of a point on the rim and at a point halfway to the center

Solution:

As per the given criteria,

$d=1m,r_T=r=0.5m,N=120rev/min$ for $r_P=\frac{r}{2}=0.25m$

We know

$\omega =\frac{2\pi N}{60}=\frac{2\times \pi \times 120}{60}⟹\omega =4\pi =12.56rad/s$

The linear speed of the point on the rim is

$v_T=t_T\omega =0.5\times 12.56=6.28m/s$

$v_P=r_P\omega =0.25\times 12.56=3.14m/s$

Hence angular speed of the point on the rim = 12.57 rad/ velocity of the point on the rim = 6.28m/s,

Angular speeed of the the point on halfway = 12.57m/s, linear velocity of the point on halfway = 3.14m/s