Angular Acceleration of game show wheel

In summary, a wheel on a game show with an initial angular speed of 1.22 rad/s comes to rest after rotating through 3/4 of a turn. To find the average torque exerted on the wheel, conservation of rotational kinetic energy is used and the torque is found to be 0.255 N*m.
  • #1
tsdemers
3
0
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?
 
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  • #2
tsdemers said:
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 = [itex]\tau \Delta \theta[/itex] = Energy available = [itex]\frac{1}{2}I\omega^2[/itex]

AM
 
  • #3
tsdemers said:
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} = ωf = (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*(ωf)2 - (1/2)*I*(ω0)2
::: ⇒ τ*θ = (1/2)*I*{(ωf)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)


~~
 
  • #4
Thank you

Thank you for the help. It's greatly appreciated :smile:
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It measures how quickly the rotational speed of an object is changing.

2. How is angular acceleration different from linear acceleration?

Angular acceleration is specific to rotational motion, while linear acceleration is specific to linear motion. Angular acceleration measures how quickly the rotational speed of an object is changing, while linear acceleration measures how quickly the linear speed of an object is changing.

3. How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is: α = (ω2 - ω1) / (t2 - t1), where α is angular acceleration, ω is angular velocity, and t is time.

4. How does angular acceleration affect the motion of a game show wheel?

Angular acceleration affects the speed and direction of the game show wheel's rotation. If the wheel experiences a positive angular acceleration, it will speed up its rotation in a clockwise direction. If it experiences a negative angular acceleration, it will slow down its rotation in a counterclockwise direction.

5. What factors can affect the angular acceleration of a game show wheel?

The angular acceleration of a game show wheel can be affected by the force applied to it, the moment of inertia of the wheel, and the friction between the wheel and its axle. Any changes in these factors can result in a change in the angular acceleration of the wheel.

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