A 0.20-m radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s. What is the average tangential acceleration of a point on the wheel's edge?Select one:a.0.45 m/s2b.28 m/s2c.0.60 m/s2d.14 m/s2
Question
A 0.20-m radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s. What is the average tangential acceleration of a point on the wheel's edge?Select one:a.0.45 m/s2b.28 m/s2c.0.60 m/s2d.14 m/s2
Solution
The average tangential acceleration (a_t) can be calculated using the formula:
a_t = r * α
where r is the radius of the wheel and α is the angular acceleration.
First, we need to find the angular acceleration. Angular acceleration (α) can be calculated using the formula:
α = Δω / Δt
where Δω is the change in angular velocity and Δt is the change in time.
Given that the wheel starts at rest (initial angular velocity, ω_i = 0 rad/s) and develops an angular speed of 12.0 rad/s (final angular velocity, ω_f = 12.0 rad/s) in 4.0 s (Δt = 4.0 s), we can substitute these values into the formula to find α:
α = (ω_f - ω_i) / Δt α = (12.0 rad/s - 0 rad/s) / 4.0 s α = 3 rad/s²
Now that we have α, we can substitute it and the given radius (r = 0.20 m) into the formula for a_t:
a_t = r * α a_t = 0.20 m * 3 rad/s² a_t = 0.60 m/s²
So, the average tangential acceleration of a point on the wheel's edge is 0.60 m/s². Therefore, the correct answer is c. 0.60 m/s².
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