A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate: What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!) What is the resulting angular acceleration of the wheel? What is the angular velocity of the wheel when the suitcase hits the ground? What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!) What is the torque caused by that tension? What is the moment of inertia of the wheel?
A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate: What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!) What is the resulting angular acceleration of the wheel? What is the angular velocity of the wheel when the suitcase hits the ground? What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!) What is the torque caused by that tension? What is the moment of inertia of the wheel?
A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate: What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!) What is the resulting angular acceleration of the wheel? What is the angular velocity of the wheel when the suitcase hits the ground? What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!) What is the torque caused by that tension? What is the moment of inertia of the wheel?
A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate:
What is the linear acceleration of the suitcase as it falls? (Hint: It’s not in free fall!)
What is the resulting angular acceleration of the wheel?
What is the angular velocity of the wheel when the suitcase hits the ground?
What is the tension in the string as the suitcase falls? (Hint: It is not equal to the weight of the case! Use Newton’s Second Law!)
What is the torque caused by that tension?
What is the moment of inertia of the wheel?
Transcribed Image Text:### Diagram Description: Pulley System with a Suitcase
This image illustrates a simple mechanical system involving a pulley and a suspended suitcase.
- **Pulley**: At the top of the image is a large wheel representing a pulley, which is depicted in light brown. The pulley allows the rope to move freely without friction.
- **Rope and Suitcase**: A rope runs over the pulley, connected to a suitcase depicted in orange. The suitcase is suspended in the air.
- **Distance Measurement**: There is a dashed line originating from the bottom of the suitcase to the ground, indicating a vertical distance of 4.00 meters. This shows how high the suitcase is above the ground.
This diagram is an example of a basic physics problem involving gravitational potential energy, often used to study the effects of forces on stationary objects.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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