A particle, at the rim of a rotating disc of radius 1m, has a constant speed of 16m/s.What is a the tangential speed of a point at r=0.5m?a.10m/sb.8m/sc.9m/sd.11m/s
Question
A particle, at the rim of a rotating disc of radius 1m, has a constant speed of 16m/s.What is a the tangential speed of a point at r=0.5m?a.10m/sb.8m/sc.9m/sd.11m/s
Solution
The tangential speed (v) of a point on a rotating disc is given by the formula:
v = ωr
where: ω = angular velocity r = radius
The angular velocity is the same for all points on the disc. So, if we know the speed and radius of one point, we can find the angular velocity and then use it to find the speed of another point.
Given that a particle at the rim of the disc (r = 1m) has a speed of 16m/s, we can find the angular velocity:
ω = v / r ω = 16m/s / 1m ω = 16 rad/s
Now we can find the tangential speed of a point at r = 0.5m:
v = ωr v = 16 rad/s * 0.5m v = 8m/s
Therefore, the tangential speed of a point at r = 0.5m is 8m/s.
The correct answer is:
b. 8m/s
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