Answer:
Time taken t=6.614s
Explanation:
Initial angular velocity ωi=120 rev/min= 12.5664 rad/s
Final angular velocity ωf=0
Angular acceleration a= -1.90 rad/s²
To find
Time taken
Solution
We can find time from angular velocity as:
Δω=at
[tex]t=\frac{w_{f}-w_{i} }{a}\\t=\frac{0-12.5664rad/s }{-1.90rad/s^{2}}\\ t=6.614s[/tex]
Answer:
6.48s
Explanation:
Angular acceleration/deceleration (α) is the time rate of change in angular velocity (ω). Mathematically,
α = Δω / t
α = (ω₂ - ω₁) / t ----------------------------(i)
where,
α = angular acceleration / deceleration
ω₂ = final angular velocity
ω₁ = initial angular velocity
t = time taken.
From the question,
α = angular deceleration = -1.94rad/s² (negative sign since its decelerating)
ω₂ = final angular velocity = 0 (since the grinding wheel comes to a stop)
ω₁ = initial angular velocity = 120rev/min
Convert 120rev/min to rad/s
Remember,
1 rev = 2π rad and
1 min = 60 s
=> 120rev/min = [tex]\frac{120 rev}{1 min}[/tex] = [tex]\frac{120* 2\pi rad}{60s}[/tex] = 12.5664rad/s
Substitute the values of α, ω₂ and ω₁ into equation (i)
=> -1.94 = (0 - 12.5664) / t
=> -1.94 = -12.5664 / t
Solving for t;
=> t = -12.5664 / -1.94
=> t = 6.48s
Therefore, the time it takes for the grinding to stop is 6.48s
