A CD has a mass of 17.4 g and a radius of 6.01 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 20.0 rad/s in 0.901 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.
torque*radius=momentinertia*angular acceleration.
I am not certain what your question about this is.
To determine the net torque acting on the CD, we need to use the equation relating torque, moment of inertia, and angular acceleration.
The moment of inertia for a uniform solid disk rotating about its center is given by the formula:
I = (1/2) * m * r^2
Where:
- I represents the moment of inertia
- m is the mass of the CD
- r is the radius of the CD
Given:
- m = 17.4 g = 0.0174 kg
- r = 6.01 cm = 0.0601 m
First, we need to calculate the moment of inertia of the CD:
I = (1/2) * 0.0174 kg * (0.0601 m)^2
Next, we need to calculate the angular acceleration (α) of the CD:
α = (Δω) / Δt
Given:
Δω = 20.0 rad/s (angular velocity)
Δt = 0.901 s
Substituting the given values, we can calculate the angular acceleration:
α = (20.0 rad/s - 0 rad/s) / 0.901 s
Now, we have the moment of inertia (I) and the angular acceleration (α), so we can calculate the net torque (τ):
τ = I * α
Substituting the values, we get:
τ = [(1/2) * 0.0174 kg * (0.0601 m)^2] * [(20.0 rad/s - 0 rad/s) / 0.901 s]
Now, you can calculate the net torque acting on the CD by plugging in the values and performing the necessary calculations.