What is the Minimum Tangential Velocity to Land on $1.00 on Wheel of Fortune?

In summary, the contestant on the wheel of fortune must have a minimum tangential velocity of 3.008m/s in order to reach the $1.00, assuming a deceleration of 0.400 rad/s2 and starting 4 positions away from the $1.00. The contestant must also take into account the direction they are spinning in, as it may affect the number of intervals they need to travel.
  • #1
Extremist223
7
0

Homework Statement


The wheel of fortune wheel, whose radius is 3.00m, has 20 different numbers, at equal intervals, for a contestant to land on. The second contestant can spin the wheel, and wishes to land on the $1.00. The wheel starts off 4 positions away from the $1.00. Assuming a deceleration of 0.400 rad/s2, what must be the minimum tangential velocity for the contestant to reach the $1.00, if they pull the wheel down?

Homework Equations


2pi rads is a full circle
w^2 = wo^2 + 2(alpha)(theta)
alpha= angular acceleration
theta is distance in radians travelled
w^2 is final angular velocity squared
wo^2 is initial angular velocity squared
Tangential Velocity = Radius x w

The Attempt at a Solution


2pi/20= 0.314 rads per interval
the goal is 4 intervals away from the start therefore 4x0.314= 1.257 rads travelled.
it wants to land 4 intervals away from the start so the final angular velocity = 0 rad/s
therefore w^2 = wo^2 + 2 (alpha)(theta)
0 = wo^2 + 2(-.4rad/s^2)(1.257)
-wo^2= -1.0056rad/s
wo^2 = 1.0056rad/s
wo= 1.00265rad/s
so at this point i took vt= rw vt= 3m x 1.00265rad/s vt = 3.008m/s

I'm getting the answer wrong and I don't know why. Can anyone help me please?
 
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  • #2
It could be that you are really 16 spaces away because of the direction you are required to spin in. Looks okay otherwise.
 
  • #3
thanks it seems to be the case one of the multiple choice answers is very close to this, but since it doesn't specify where on the wheel it is being pulled down from left side or right side this question is ambiguous
 

Related to What is the Minimum Tangential Velocity to Land on $1.00 on Wheel of Fortune?

1. What is rotational kinematics?

Rotational kinematics is a branch of physics that deals with the motion of objects that are rotating or moving in a circular or curved path.

2. What are the basic quantities used in rotational kinematics?

The basic quantities used in rotational kinematics are angular displacement, angular velocity, and angular acceleration. These quantities are similar to their linear counterparts (displacement, velocity, and acceleration) but are measured in radians and radians per second instead of meters and meters per second.

3. What is the difference between angular velocity and linear velocity?

Angular velocity refers to the rate at which an object is rotating, while linear velocity refers to the rate at which an object is moving in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

4. How is rotational kinematics related to rigid body dynamics?

Rotational kinematics is a fundamental concept in rigid body dynamics, which is the study of the motion of objects that are not deformable. Rigid body dynamics uses rotational kinematics to analyze the motion of objects that are rotating or moving in a circular path, such as wheels, gears, and pulleys.

5. Can rotational kinematics be applied to non-circular motion?

Yes, rotational kinematics can be applied to non-circular motion, such as objects moving in an elliptical or parabolic path. In these cases, the angular displacement, velocity, and acceleration will vary at different points along the path, but the same principles of rotational kinematics still apply.

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