The angular velocity of a particle rotating in a circular orbit 100 times per minute is:
Correct answer: B. 10.47rad/s
- A. 1.66rad/s
- B. 10.47rad/s
- C. 10.47deg/s
- D. 60deg/s
Explanation
The following is the solution:The angular velocity of the particle rotating in a circular orbit 100 times per minute is:ω = 2πfwhere f is the frequency of rotation in hertz.In this case, the frequency of rotation is 100 times per minute. Converting this to hertz, we get:f = 100/60 = 5/3 HzSubstituting this value into the formula for angular velocity, we get:ω = 2πf = 2π(5/3) = 10π/3 radians per secondApproximating this value to two decimal places, we get:ω ≈ 10.47 radians per secondTherefore, the angular velocity of the particle rotating in a circular orbit 100 times per minute is approximately 10.47 radians per second.
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About Angular Velocity
Angular velocity describes how quickly angular displacement changes with time, with ω = Δθ/Δt and units of radians per second. Questions relate angular and linear motion through v = rω, use the direction given by the right hand rule, and distinguish angular velocity from angular acceleration and ordinary frequency.
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