A point on the rim of a 0.75 m diameter grinding wheel changes speed at a constant rate from 15 m/s to 21 m/s in 6.2 s. What is the average angular acceleration of the wheel in rad/s^2?
Divide the angular velocity change by the time interval required for that change.
The angular velocity change is
delta w = (21 - 15)/R = 8.0 rad/s
Divide that by 6.2 s
please give me answer
To find the average angular acceleration of the grinding wheel, we can use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
First, let's calculate the initial and final angular velocities of the grinding wheel.
The diameter of the grinding wheel is given as 0.75 m. The radius of the wheel can be calculated by dividing the diameter by 2:
Radius (r) = Diameter / 2
r = 0.75 m / 2
r = 0.375 m
The initial and final speeds of the point on the rim of the wheel are given as 15 m/s and 21 m/s, respectively.
The initial angular velocity (ω₁) can be calculated using the formula:
ω₁ = v₁ / r,
where v₁ is the initial speed and r is the radius.
ω₁ = 15 m/s / 0.375 m
ω₁ = 40 rad/s
Similarly, the final angular velocity (ω₂) can be calculated using the formula:
ω₂ = v₂ / r,
where v₂ is the final speed and r is the radius.
ω₂ = 21 m/s / 0.375 m
ω₂ = 56 rad/s
Now, we can use the formula for angular acceleration to calculate the average angular acceleration:
α = (ω₂ - ω₁) / t,
where ω₂ is the final angular velocity, ω₁ is the initial angular velocity, and t is the time.
α = (56 rad/s - 40 rad/s) / 6.2 s
α ≈ 2.58 rad/s²
Therefore, the average angular acceleration of the grinding wheel is approximately 2.58 rad/s².