A rotating wheel as an initial angular velocity of 10rad/s and 2.5rad/s^2.how many revolution does it will complete in 30seconds?
angular displacement=avgspeed*time=(1/2)(10+2.5)*30
In rotations, divide by 2PI
For accelerated motion
2πN = ω(o)t +εt^2/2,
N =t (ω(o) +0.5εt)/2π=
= 30•(10+0.5•2.5•30)/2•3.14 =226.8 rev
To find the number of revolutions the rotating wheel will complete in 30 seconds, we need to understand the relationship between angular velocity, angular acceleration, and time.
The formula to calculate the displacement (θ) of an object undergoing rotational motion is given by:
θ = ωi * t + (1/2) * α * t^2
Where:
- θ is the displacement (in radians)
- ωi is the initial angular velocity (in radians per second)
- t is the time (in seconds)
- α is the angular acceleration (in radians per second squared)
In this case, we have:
ωi = 10 rad/s
α = 2.5 rad/s^2
t = 30 seconds
Substituting these values into the formula, we get:
θ = (10 * 30) + (1/2) * 2.5 * (30^2)
= 300 + (15 * 900)
= 300 + 13500
= 13800 radians
To convert this to revolutions, we need to divide the displacement by 2π (since there are 2π radians in one revolution):
Number of revolutions = θ / (2π)
= 13800 / (2π)
≈ 2197 revolutions
Therefore, the rotating wheel will complete approximately 2197 revolutions in 30 seconds.