A DVD player can exert a torque on a DVD of 10−3 N⋅m. What is the DVD’s angular acceleration in rad/s2?
To find the DVD's angular acceleration, we need to use the formula for torque:
Torque (τ) = Moment of inertia (I) × Angular acceleration (α)
Rearranging the formula, we can solve for α:
α = τ / I
Given that the torque exerted by the DVD player is 10^-3 N⋅m, we need the moment of inertia of the DVD to calculate the angular acceleration. The moment of inertia depends on the shape and mass distribution of the object.
If the DVD is considered a solid disk with a uniform mass distribution, we can use the formula for moment of inertia of a solid disk:
I = (1/2) * M * R^2
Where:
M is the mass of the DVD
R is the radius of the DVD
If the radius and mass of the DVD are provided, we can substitute the values into the formula and calculate the moment of inertia. Then, substitute the torque value and the moment of inertia into the formula for angular acceleration:
α = (10^-3 N⋅m) / I
If the radius and mass values are not provided, additional information is necessary to compute the angular acceleration.