A spotlight S rotates in horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance of 3m. The velocity of the spot P when degrees is __________ m/s.
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182
Given :
Linear Velocity of rotating object ν=ωr/sinθ
ω= angular velocity=0.1 rad/s
r-distance of object from centre.
angle=45°
r=d/cosθ [ where d is the distance from the spot light to wall] =3/cos45°
Velocity= ν=ωr/sinθ
=[0.1x3/cos45°]/sin45°
=0.1x3/sin45 °cos45°
= 0.3/[1√2 x 1 /2]
=2x0.3
=0.6m/s
∴The velocity of the spot P is 0.6 m/s
Linear Velocity of rotating object ν=ωr/sinθ
ω= angular velocity=0.1 rad/s
r-distance of object from centre.
angle=45°
r=d/cosθ [ where d is the distance from the spot light to wall] =3/cos45°
Velocity= ν=ωr/sinθ
=[0.1x3/cos45°]/sin45°
=0.1x3/sin45 °cos45°
= 0.3/[1√2 x 1 /2]
=2x0.3
=0.6m/s
∴The velocity of the spot P is 0.6 m/s
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Answer:
0.6 m/s
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