Question

a spot light rotates in a horizonta plane with a constant angular velocity. A spot of light P moves along wall. The velocity of spot along the wall is 6m/s,when spot light is rotated by 45degree .what is angular velocity of spot light??
(a) 1rad/s (b) 2rad/s (c)0.5rad/s (d)0.1rad/s

Answer 1

Answer on Question #40823, Physics, Mechanics

A spot light S rotates in a horizontal plane with a constant angular velocity. A spot of light P moves along wall. The velocity of spot along the wall is $6\mathrm{m / s}$ , when spot light is rotated by 45 degree. What is angular velocity of spot light??

(a) 1rad/s

(b) 2rad/s

(c)0.5rad/s

(d)0.1rad/s

Solution:

The rate of change of angular displacement of the particle in a given time is called angular velocity. It is expressed as

$$\omega = \frac {\theta}{t}$$

Where $\theta$ is angular displacement and $t$ is the time taken.

$\theta = 45{}^{\circ} = 45{}^{\circ}\cdot \pi /180$ rad $= 45\cdot 3.14 / 180 = 0.785$ rad.

The time t is

$$t = \frac {d}{v}$$

where $d$ is linear displacement and $v$ is the velocity of spot.

For our case $(\theta = 45{}^{\circ})$ the d is equal to the distance to a wall.

Thus,

$$\omega = \frac {\theta}{t} = \frac {\theta v}{d}$$ $$\omega = \frac {0 . 7 8 5 \cdot 6}{d} = \frac {4 . 7 1}{d} \mathrm {r a d / s}.$$

Answer. $\omega = \frac{4.71}{d}$ .