A ceiling fan is turned on and a net torque of 1.6 N·m is applied to the blades. The blades have a total moment of inertia of 0.25 kg·m2. What is the angular acceleration of the blades?
angular acceleration
= (Torque)/(moment of inertia)
The units will be radians/s^2 if torque and moment of inertia are in the units given.
Answer
Well, let's see if I can put a humorous spin on this one. The angular acceleration of the blades can be calculated using the formula τ = Iα, where τ is the net torque, I is the moment of inertia, and α is the angular acceleration.
Given that the net torque is 1.6 N·m and the moment of inertia is 0.25 kg·m2, we can rearrange the formula to solve for α:
α = τ / I
Plugging in the values, we get:
α = 1.6 N·m / 0.25 kg·m2
Doing the math, we find that the angular acceleration of the blades is 6.4 rad/s².
So, there you have it. The blades are getting quite a twist with an angular acceleration of 6.4 rad/s². Just make sure to keep your eyes peeled for any flying clowns while you enjoy the breeze!
To find the angular acceleration of the blades, we can use the equation:
τ = I * α
Where τ is the net torque applied to the blades, I is the moment of inertia, and α is the angular acceleration.
Plugging in the given values, we have:
1.6 N·m = 0.25 kg·m^2 * α
Now we can solve for α:
α = 1.6 N·m / 0.25 kg·m^2
= (1.6 / 0.25) (N·m / kg·m^2)
= 6.4 (N·m / kg·m^2)
Therefore, the angular acceleration of the blades is 6.4 N·m / kg·m^2.
To find the angular acceleration of the blades, you can use the formula relating torque (τ) and moment of inertia (I) to angular acceleration (α):
τ = I * α
In this case, the given net torque is 1.6 N·m and the moment of inertia is 0.25 kg·m². Substituting these values into the equation:
1.6 N·m = 0.25 kg·m² * α
To solve for α, divide both sides of the equation by 0.25 kg·m²:
α = 1.6 N·m / 0.25 kg·m²
Simplifying the equation gives:
α = 6.4 N·m /kg·m²
Therefore, the angular acceleration of the blades is 6.4 N·m /kg·m².