An electric motor rotating a workshop grind- ing wheel at a rate of 147 rev/min is switched off with a constant deceleration of 1.24 rad/s2.

How long does it take for the grinding wheel to stop?
Answer in units of s

Through how many radians has the wheel turned during the deceleration?
Answer in units of rad

change rev/min to rev/second

then, wf=wi+at where a=-1.24r/s^2
solve for t.

Dfinal(in radians)=wi*t+1/2 a t^2

To find the time it takes for the grinding wheel to stop, we can use the equation of motion:

ω = ω0 + αt

Where:
ω = final angular velocity (which is 0 since the wheel stops)
ω0 = initial angular velocity (147 rev/min)
α = deceleration (-1.24 rad/s²)
t = time

First, we need to convert the initial angular velocity from rev/min to rad/s:

1 rev = 2π rad
1 min = 60 s

So, the initial angular velocity in rad/s is:
ω0 = (147 rev/min) * (2π rad/rev) * (1 min/60 s)
ω0 = 15.4 rad/s

Now we can use the equation to find the time it takes for the wheel to stop:

0 = 15.4 rad/s + (-1.24 rad/s²) * t

Rearranging the equation, we have:

1.24t = 15.4

Solving for t:

t = 15.4 / 1.24
t ≈ 12.42 seconds

Therefore, it takes approximately 12.42 seconds for the grinding wheel to stop.

To find the number of radians the wheel has turned during the deceleration, we can use the equation:

θ = ω0t + (1/2)αt²

Where:
θ = rotation in radians
ω0 = initial angular velocity (15.4 rad/s)
α = deceleration (-1.24 rad/s²)
t = time (12.42 s)

Plugging in the values, we have:

θ = (15.4 rad/s) * (12.42 s) + (1/2) * (-1.24 rad/s²) * (12.42 s)²

Evaluating the expression:

θ ≈ 191.4 radians

Therefore, the wheel has turned approximately 191.4 radians during the deceleration.