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  2. AP Physics 1 Revised
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What are the differences between rotational and translational kinetic energy?

Rotational: Energy due to rotation, depends on moment of inertia and angular velocity. Translational: Energy due to linear motion, depends on mass and linear velocity.

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What are the differences between rotational and translational kinetic energy?

Rotational: Energy due to rotation, depends on moment of inertia and angular velocity. Translational: Energy due to linear motion, depends on mass and linear velocity.

What are the differences between scalar and vector quantities?

Scalar: Magnitude only (e.g., rotational kinetic energy). Vector: Magnitude and direction (e.g., angular velocity, angular momentum).

What are the differences between moment of inertia for a solid sphere and a hollow sphere?

Solid Sphere: I=(2/5)MR2I = (2/5)MR^2I=(2/5)MR2 (mass concentrated closer to the center). Hollow Sphere: I=(2/3)MR2I = (2/3)MR^2I=(2/3)MR2 (mass distributed further from the center).

What are the differences between rolling with slipping and rolling without slipping?

Rolling without slipping: v=Rωv = Rωv=Rω (linear and angular velocities are related). Rolling with slipping: v≠Rωv ≠ Rωv=Rω (linear and angular velocities are independent).

What are the differences between angular momentum and rotational kinetic energy?

Angular Momentum: Vector quantity, measures the quantity of rotation. Rotational Kinetic Energy: Scalar quantity, measures the energy of rotation.

How do you calculate total kinetic energy for a rolling object?

  1. Calculate rotational kinetic energy: Krot=(1/2)Iω2K_{rot} = (1/2)Iω^2Krot​=(1/2)Iω2. 2. Calculate translational kinetic energy: Ktrans=(1/2)mv2K_{trans} = (1/2)mv^2Ktrans​=(1/2)mv2. 3. Add them together: Ktotal=Krot+KtransK_{total} = K_{rot} + K_{trans}Ktotal​=Krot​+Ktrans​.

What are the steps to solve a rotational kinetic energy problem?

  1. Identify knowns and unknowns. 2. Choose the appropriate formula. 3. Convert units to radians per second if necessary. 4. Substitute values and solve.

How do you apply conservation of energy in rotational motion problems?

  1. Identify initial and final states. 2. Determine potential and kinetic energies at each state. 3. Apply the conservation of energy equation: Einitial=EfinalE_{initial} = E_{final}Einitial​=Efinal​. 4. Solve for the unknown variable.

How to calculate the rotational kinetic energy of a system with a stationary center of mass?

  1. Determine the rotational inertia (I) of the system about its center of mass. 2. Measure or calculate the angular velocity (ω) of the system. 3. Apply the formula: Krot=(1/2)Iω2K_{rot} = (1/2)Iω^2Krot​=(1/2)Iω2.

How do you relate linear and angular velocity in rolling motion?

  1. Identify the radius (R) of the rolling object. 2. Determine the angular velocity (ω) in radians per second. 3. Use the equation: v=Rωv = Rωv=Rω to find the linear velocity (v).

What happens when a torque is applied to a rotating object?

The rotational kinetic energy of the object changes (Work-Energy Theorem).

What is the effect of increasing the angular velocity of an object?

The rotational kinetic energy increases (quadratically).

What happens if a rolling object's initial potential energy is converted into both translational and rotational kinetic energy?

The object's linear speed at the bottom of the incline will be less than if all potential energy was converted to translational kinetic energy.

What is the effect of increasing the moment of inertia of a rotating object?

The rotational kinetic energy increases, assuming angular velocity remains constant.

What happens when non-conservative forces (e.g., friction) are present in a rotational system?

Total mechanical energy (including rotational kinetic energy) is not conserved.