A wheel has turned through 120 revs in 10 s after starting. find the angular acceleration.
Va = 120revs/10s * 6.28rad/rev = 75.36 rad/s. = Angular velocity.
a = (V-Vo)/t = (75.36-0)/10=7.54 rad/s^2
To find the angular acceleration, we need to first determine the change in angular velocity and the time it took for this change to occur.
Angular velocity is a measure of how fast an object is rotating. It is given by the formula:
Angular Velocity (ω) = (Change in Angle) / (Change in Time)
In this case, the wheel has turned through 120 revolutions. Since one revolution is equal to 2π radians, the change in angle can be calculated as:
Change in Angle (θ) = 120 revolutions * 2π radians/revolution
Next, we need to determine the change in time. In the problem, it is stated that the wheel turned through 120 revolutions in 10 seconds. This means that the change in time is 10 seconds.
Substituting these values into the formula for angular velocity, we have:
ω = (120 * 2π) / 10
Now, we can find the angular acceleration, which is the rate of change of the angular velocity. It is given by the formula:
Angular Acceleration (α) = (Change in Angular Velocity) / (Change in Time)
Since we are not given any additional information about the wheel's motion, we assume that it started from rest. Therefore, the initial angular velocity is zero.
Using the formula for angular acceleration, we have:
α = ω / t
Substituting the calculated value of ω and the given value of t, we find:
α = [(120 * 2π) / 10] / 10
Simplifying the expression, we get:
α = (24π) / 100
Therefore, the angular acceleration is (24π) / 100 or approximately 0.76 radians per second squared.