A torque of 12 N ∙ m is applied to a solid, uniform disk of radius If the disk accelerates at what is the mass of the disk?
torque=moment of inertia disk*alpha
To find the mass of the disk, we need to use the formula for torque and the formula for rotational inertia:
Torque = (moment of inertia) * (angular acceleration)
The moment of inertia for a solid disk rotating about its central axis is given by:
I = (1/2) * m * r^2
Where:
- I is the moment of inertia
- m is the mass of the disk
- r is the radius of the disk
In this case, we are given the torque as 12 N*m and the angular acceleration as a. We can rewrite the formula for torque as:
12 N*m = (1/2) * m * r^2 * a
We can rearrange this equation and solve for the mass of the disk:
m = (12 N*m) / [(1/2) * r^2 * a]
Substituting the given values, we can determine the mass of the disk.
To find the mass of the disk, we can start by using the formula for torque and the formula for rotational inertia (moment of inertia) of a solid disk:
Torque (τ) = Moment of Inertia (I) × Angular Acceleration (α)
The formula for the moment of inertia of a solid disk is:
Moment of Inertia (I) = (1/2) × Mass (m) × Radius^2
Given that the torque (τ) is 12 N∙m and the radius (r) is unknown, we need to determine the value of the radius first. The radius is missing from the information provided in your question, so we cannot directly determine the mass of the disk. Please provide the radius value so we can continue with the calculations.