physics questions----

Question

3.A softball player swings a bat, accelerating it from rest to 3.0 rev/s in a time of 0.20 s. Approximate the bat as a 2.2 kg uniform rod of length 0.95 m, and compute the torque the player applies to it. Answer in Nm

Answer 1

Hi Edwin W.!

Let's start with what we were given:

ω_o = 0 rad*s^-1

ω_f = 3.0 rev*s^-1

Δt = 0.20 s

mass of the bat = 2.2 kg

length of the bat = 0.95 m

The expression describing the mass moment of inertia for the bat is:

I = (1/3)ml²

<=> (1/3)(2.2kg)(0.95m)²

I = 0.662 kg*m²

Next, we need to convert the final angular speed from revolutions per second into radians per second:

(3.0 rev/s)*(2π rad/1 rev)

ω_f = 18.8 rad*s^-1

Now, we want to find the angular acceleration. We can make good use of this equation:

ω_f = ω_o + αt => α = (ω_f - ω_o)/t

=> ω_o = 0 because the bat starts from rest

α = ω_f/t

<=> 18.8 rad*s^-1/0.20 s

α = 94.2 rad*s^-2

Now that we know both the moment of inertia and the angular acceleration, we can use one of our equations for torque:

Τ = I x α

<=> (0.662 kg*m²)(94.2 rad*s^-2)

Τ = 62 N*m

Hope this helps!

Please let me know what you think in the comments, or feel free to ask any follow-up questions!