Answer:
I can help you solve the sample problems involving basic circular motion equations.
Explanation:
Let's address each part step by step:
1) A festive Mardi Gras merry-go-round:
A) To find the time it takes for the merry-go-round to stop:
Equation used: \[ \text{final angular velocity} = \text{initial angular velocity} + \text{angular acceleration} \times \text{time} \]
\[ 0 = 25 \text{ rotations/min} - 0.5 \text{ rad/s}^2 \times \text{time} \]
Solving for time gives: \[ \text{time} = \frac{25 \text{ rotations/min}}{0.5 \text{ rad/s}^2} \times \frac{2\pi \text{ rad}}{1 \text{ rotation}} \times \frac{1 \text{ min}}{60 \text{ s}} \]
B) To determine the number of rotations during this time:
\[ \text{rotations} = \text{initial angular velocity} \times \text{time} + 0.5 \times \text{angular acceleration} \times \text{time}^2 \]
C) To find the linear acceleration of a point on the edge:
\[ \text{linear acceleration} = \text{radius} \times \text{angular acceleration} \]
D) For initial and final linear velocities:
Initial linear velocity: \[ \text{initial linear velocity} = \text{initial angular velocity} \times \text{radius} \]
Final linear velocity: \[ \text{final linear velocity} = 0 \]
E) The arc length that a point on the edge moves:
\[ \text{arc length} = \text{radius} \times \text{angle in radians} \]
2) A) For the electric motor spinning the silver platter:
To find initial and final angular velocities:
\[ \text{final angular velocity} = \text{initial angular velocity} + \text{angular acceleration} \times \text{time} \]
B) Maximum distance the center of mass of the food can sit from the middle of the platter:
Use the relation between linear and angular velocity: \[ \text{linear velocity} = \text{radius} \times \text{angular velocity} \]
By following these steps and equations, you can solve the given sample problems on circular motion effectively.
