The wheel of Fortune. a contestant gives the wheel an initial angular velocity of -5.95 rad/s and the wheel stops after 5.8s of constant acceleration.
Determine the panel (e.g. $600 or bankrupt) that the yellow pointer will be on when the wheel stops.
Angular Displacement(red)———-panel value and color———
I need help with this there is picture in the question but I couldn’t put it ? Any help please thanks
Anyone???
the average angular velocity is half of the initial
the wheel will travel ... -5.95 rad/sec * 5.8 sec / 2 ... radians
To determine the panel that the yellow pointer will be on when the wheel stops, we need to use the equations of rotational motion.
Let's break down the problem into steps:
Step 1: Convert the initial angular velocity to the correct units.
The given initial angular velocity is -5.95 rad/s. Since the direction is not relevant for this problem, we can consider the magnitude only.
Step 2: Determine the final angular velocity using the equation:
ωf = ω0 + αt
where ω0 is the initial angular velocity, α is the constant angular acceleration, and t is the time interval.
Rearranging the equation, we have:
ωf = -5.95 rad/s + α(5.8s)
Step 3: Solve for α (angular acceleration).
To find α, we need more information. If the problem does not provide it, we won't be able to determine the panel value and color.
Step 4: Determine the final angular displacement using the equation:
θf = ω0t + 0.5αt^2
where θf is the final angular displacement, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time interval.
Substituting the given values, we have:
θf = -5.95 rad/s * 5.8s + 0.5α(5.8s)^2
Step 5: Convert the angular displacement into a panel value and color.
Unfortunately, without the angular acceleration (α), we cannot determine the final angular displacement or the panel value and color that the yellow pointer will be on when the wheel stops.
If you have the value for angular acceleration (α) or any additional information, please provide it so we can continue to solve the problem using the given data.