A car wheel has a moment of inertia of 0.35kg m^2. It takes 50 seconds to come to rest from the initial angular velocity of 45 rpm. Calculate the magnitude of the average friction torque
torque=I*(45*2PI/60)/50
To calculate the magnitude of the average friction torque, we can use the following formula:
Friction Torque = Change in Angular Momentum / Time
Given:
Moment of Inertia (I) = 0.35 kg m^2
Initial Angular Velocity (ωi) = 45 rpm = 45 revolutions/minute
Final Angular Velocity (ωf) = 0 (since it comes to rest)
Time (t) = 50 seconds
First, let's convert the initial angular velocity from rpm to rad/s:
ωi = (45 rpm) * (2π rad/1 rev) * (1 min/60 s)
= 4.7124 rad/s
Next, we can calculate the change in angular momentum using the formula:
Change in Angular Momentum (ΔL) = I * (ωf - ωi)
ΔL = (0.35 kg m^2) * (0 - 4.7124 rad/s)
= -1.6498 kg m^2/s
Finally, we can substitute the values into the formula to calculate the average friction torque:
Friction Torque = ΔL / t
Friction Torque = (-1.6498 kg m^2/s) / (50 s)
= -0.033 kg m^2/s^2
The magnitude of the average friction torque is 0.033 kg m^2/s^2.
To calculate the magnitude of the average friction torque, we need to use the formula:
Friction Torque (τ) = Change in Angular Momentum / Change in Time
First, we need to find the change in angular momentum. Angular momentum (L) is given by:
Angular Momentum (L) = Moment of Inertia (I) × Angular Velocity (ω)
The initial angular velocity (ω_i) is given as 45 rpm. However, we need to convert it to rad/s to use it in the formula. Since 1 revolution is equal to 2π radians, we can convert rpm to rad/s by multiplying by 2π/60:
ω_i = (45 rpm) × (2π rad/1 rev) × (1 rev/60 s) ≈ 4.71 rad/s
We are given the moment of inertia (I) as 0.35 kg m^2.
Now, let's find the final angular velocity (ω_f). We know that the car wheel comes to rest, which means the final angular velocity will be 0 rad/s.
Using the formula for change in angular momentum:
Change in Angular Momentum (ΔL) = L_f - L_i = 0 - (I × ω_i)
Now, let's find the change in time (Δt) which is given as 50 seconds.
Finally, we can substitute the values into the formula for friction torque:
Friction Torque (τ) = (ΔL) / (Δt)
Substituting the values:
τ = -(I × ω_i) / Δt
τ = - (0.35 kg m^2) × (4.71 rad/s) / (50 s) ≈ -0.033 Nm
Note: The negative sign indicates that the direction of the torque is opposite to the initial angular velocity. The absolute value of the friction torque is 0.033 Nm.