A particle is located on the edge of a rotating wheel with a uniform angular speed of 4 radians per second. If the particle is 0.3 meters from the center of the wheel, calculate the tangential speed of the particle.
Question
A particle is located on the edge of a rotating wheel with a uniform angular speed of 4 radians per second. If the particle is 0.3 meters from the center of the wheel, calculate the tangential speed of the particle.
Solution
The tangential speed (v) of a particle moving in a circular path is given by the formula:
v = rω
where: r is the radius of the circular path (in meters), and ω is the angular speed (in radians per second).
In this case, the radius r is 0.3 meters and the angular speed ω is 4 radians per second.
Substituting these values into the formula gives:
v = 0.3 m * 4 rad/s = 1.2 m/s
So, the tangential speed of the particle is 1.2 meters per second.
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