a wheel 0.45m in diameter starts from rest and rotates with uniform acceleration to 6000 radians per minute in a time of 4s.Find angular acceleration of the wheel and speed of a point on the rim at end of 4s =w/t
Vo = 0
V = 6,000rad/min = 6,000rad/60s = 100 rad/s.
a = (V-Vo)/t = (100-0)/4 = 25 rad/s^2
To find the angular acceleration of the wheel, we need to use the formula:
Angular Acceleration (α) = (Final Angular Velocity - Initial Angular Velocity) / Time
Given that the wheel starts from rest (Initial Angular Velocity = 0 radians/minute), the final angular velocity is 6000 radians/minute, and the time taken is 4 seconds, we can plug these values into the formula to calculate the angular acceleration.
Angular Acceleration (α) = (6000 radians/minute - 0 radians/minute) / 4 seconds
Now, we need to convert the angular acceleration from radians/minute to radians/second. There are 60 seconds in a minute, so we can convert the angular acceleration by dividing it by 60.
Angular Acceleration (α) = (6000 radians/minute - 0 radians/minute) / 4 seconds * (1 minute / 60 seconds)
After simplifying, we get:
Angular Acceleration (α) = (6000 / 4) * (1/60) radians/second
= (1500/60) radians/second
= 25 radians/second
Therefore, the angular acceleration of the wheel is 25 radians/second.
To find the speed of a point on the rim at the end of 4 seconds, we need to use the formula:
Speed = Angular Velocity * Radius
Given that the diameter of the wheel is 0.45m, we can calculate the radius by dividing the diameter by 2.
Radius (r) = Diameter / 2
= 0.45m / 2
= 0.225m
Now, we can substitute the angular velocity (6000 radians/minute) into the formula to find the speed.
Speed = (Angular Velocity * 2π) * Radius
= (6000 radians/minute * 2π) * 0.225m
Again, we need to convert the angular velocity from radians/minute to radians/second. There are 60 seconds in a minute, so we can convert the angular velocity by dividing it by 60.
Speed = (6000/60 * 2π) * 0.225m
After simplifying, we get:
Speed = 1000π * 0.225m
= 225π m/s
Therefore, the speed of a point on the rim at the end of 4 seconds is 225π m/s.