Angular Acceleration of game show wheel

[tsdemers]

A wheel on a game show is given an initial angular speed of 1.22 rad/s. It comes to rest after rotating through 3/4 of a turn. Find the average torque exerted on the wheel given that it is a disk of radius 0.71m and a mass 6.4kg.

I'm lost. I don't really know where to begin. I know the answer is going to be 0.25Nm but I just need some help getting on the right track. Any suggestions?

 

[Andrew Mason]

A wheel on a game show is given an initial angular speed of 1.22 rad/s. It comes to rest after rotating through 3/4 of a turn. Find the average torque exerted on the wheel given that it is a disk of radius 0.71m and a mass 6.4kg.

I'm lost. I don't really know where to begin. I know the answer is going to be 0.25Nm but I just need some help getting on the right track. Any suggestions?

Use conservation of energy

Work done = $\tau \Delta \theta$ = Energy available = $\frac{1}{2}I\omega^2$

AM

 

[xanthym]

A wheel on a game show is given an initial angular speed of 1.22 rad/s. It comes to rest after rotating through 3/4 of a turn. Find the average torque exerted on the wheel given that it is a disk of radius 0.71m and a mass 6.4kg.

I'm lost. I don't really know where to begin. I know the answer is going to be 0.25Nm but I just need some help getting on the right track. Any suggestions?

From the problem statement:
{Disk Mass} = M = (6.4 kg)
{Disk Radius} = R = (0.71 m)
{Disk Moment of Inertia} = I = (1/2)*M*R² = (1/2)*(6.4)*(0.71)² = (1.613 kg*m²)
{Initial Disk Angular Speed} = ω₀ = (1.22 rad/s)
{Final Disk Angular Speed} = ω_f = (0.0 rad/s)
{Disk Angular Rotation} = θ = (3/4 Turn) = (4.712 rad)
{Torque Applied to Disk} = τ

From Conservation of Rotational Kinetic Energy:
{Rotational Work} = τ*θ = {Final Rotational Kinetic Energy} - {Initial Rotational Kinetic Energy}
::: ⇒ τ*θ = (1/2)*I*(ω_f)² - (1/2)*I*(ω₀)²
::: ⇒ τ*θ = (1/2)*I*{(ω_f)² - (ω₀)²}
::: ⇒ τ*(4.712 rad) = (1/2)*(1.613 kg*m²)*{(0.0 rad/s)² - (1.22 rad/s)²}
::: ⇒ τ*(4.712) = (-1.2)
::: ⇒ |τ| = (0.255 N*m)


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[tsdemers]

Thank you

Thank you for the help. It's greatly appreciated