Podcast
Questions and Answers
A solid disc and a hollow sphere have the same mass and radius. If both are released from rest at the top of an inclined plane and roll without slipping, which one will reach the bottom first?
A solid disc and a hollow sphere have the same mass and radius. If both are released from rest at the top of an inclined plane and roll without slipping, which one will reach the bottom first?
- The hollow sphere will reach first.
- The solid disc will reach first. (correct)
- They will reach at the same time.
- The object with higher mass will reach first
What happens to the total kinetic energy during an inelastic collision where rotational motion is involved?
What happens to the total kinetic energy during an inelastic collision where rotational motion is involved?
- Total kinetic energy is conserved.
- Total kinetic energy decreases. (correct)
- Total kinetic energy increases.
- Total kinetic energy remains constant.
A figure skater spins faster when she pulls her arms closer to her body. Which principle explains this phenomenon?
A figure skater spins faster when she pulls her arms closer to her body. Which principle explains this phenomenon?
- Conservation of linear momentum
- Newton's first law
- Conservation of angular momentum (correct)
- Conservation of energy
A wheel is rotating with a constant angular velocity. If the net torque acting on the wheel is zero, what can be said about its angular momentum?
A wheel is rotating with a constant angular velocity. If the net torque acting on the wheel is zero, what can be said about its angular momentum?
How does increasing the distance of mass distribution from the axis of rotation affect the moment of inertia of an object?
How does increasing the distance of mass distribution from the axis of rotation affect the moment of inertia of an object?
A force is applied at an angle to a door, trying to swing it open. At what angle should the force be applied to achieve maximum torque?
A force is applied at an angle to a door, trying to swing it open. At what angle should the force be applied to achieve maximum torque?
A rotating object has an initial angular velocity $\omega_0$ and undergoes constant angular acceleration $\alpha$. What is its angular displacement $\theta$ after time t?
A rotating object has an initial angular velocity $\omega_0$ and undergoes constant angular acceleration $\alpha$. What is its angular displacement $\theta$ after time t?
How is angular impulse related to torque and time?
How is angular impulse related to torque and time?
If a small, dense object and a large, less dense object have the same mass, which will typically have a larger moment of inertia if rotated around a central axis?
If a small, dense object and a large, less dense object have the same mass, which will typically have a larger moment of inertia if rotated around a central axis?
What condition must be met for linear momentum to be conserved in a collision?
What condition must be met for linear momentum to be conserved in a collision?
A student is solving a rotational kinematics problem and needs to find the final angular velocity ($\omega$). They are given the initial angular velocity ($\omega_0$), the angular acceleration ($\alpha$), and the angular displacement ($\theta$). Which equation should they use?
A student is solving a rotational kinematics problem and needs to find the final angular velocity ($\omega$). They are given the initial angular velocity ($\omega_0$), the angular acceleration ($\alpha$), and the angular displacement ($\theta$). Which equation should they use?
A toy car moves around a circular track. If the car's linear speed is constant, what can be said about its angular momentum with respect to the center of the track?
A toy car moves around a circular track. If the car's linear speed is constant, what can be said about its angular momentum with respect to the center of the track?
Two objects have the same angular momentum. Object A has a moment of inertia twice that of Object B. How do their angular velocities compare?
Two objects have the same angular momentum. Object A has a moment of inertia twice that of Object B. How do their angular velocities compare?
In what direction is positive torque conventionally defined?
In what direction is positive torque conventionally defined?
When comparing the rotational kinetic energy of two objects, what parameter has the most significant impact, assuming mass and size are similar?
When comparing the rotational kinetic energy of two objects, what parameter has the most significant impact, assuming mass and size are similar?
What best describes the concept of translational kinetic energy?
What best describes the concept of translational kinetic energy?
An object's angular momentum is conserved if the net external torque acting on it is:
An object's angular momentum is conserved if the net external torque acting on it is:
A force applied far away from the axis of rotation will generally produce ________ torque compared to the same force applied closer to the axis.
A force applied far away from the axis of rotation will generally produce ________ torque compared to the same force applied closer to the axis.
What is the relationship between linear and angular acceleration?
What is the relationship between linear and angular acceleration?
Flashcards
Rotational Kinematics
Rotational Kinematics
Relates linear and angular motion; students apply these to scenarios and graphs.
Linear to Angular Equations
Linear to Angular Equations
x=θr, v=ωr, a=αr. Relates linear displacement, velocity, and acceleration to angular counterparts.
Rotational Kinematic Equations
Rotational Kinematic Equations
θ = θ₀ + ω₀t + (1/2)αt², ω = ω₀ + αt, ω² = ω₀² + 2α(θ - θ₀).
Torque Convention
Torque Convention
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Torque and Angular Acceleration Equations
Torque and Angular Acceleration Equations
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Moment of Inertia
Moment of Inertia
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Moment of Inertia (point object)
Moment of Inertia (point object)
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Multiple Moments of Inertia
Multiple Moments of Inertia
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Total Kinetic Energy (rolling object)
Total Kinetic Energy (rolling object)
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Angular Momentum
Angular Momentum
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Angular Momentum Equations
Angular Momentum Equations
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Angular Momentum Conservation
Angular Momentum Conservation
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Inelastic Collisions (KE)
Inelastic Collisions (KE)
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Study Notes
Rotational Kinematics
- Students can translate between linear and angular equations.
- x=Θr
- V=⍵r
- a= ⍺r
Torque and Angular Acceleration
- Convention: Clockwise torque is negative, while counter-clockwise torque is positive.
- Net Torque is the sum of individual torques acting.
- Moment of Inertia is larger when mass is distributed toward outer dimensions and when radius is larger (I ∝ m R2).
- For a point object, I ∝ m R2, which allows conversion between linear and angular momentum.
- For multiple Moments of Inertia, they are added for the I value in 𝜏 = I ⍺.
Kinetic Energy and Energy Conservation
- When an object rolls, there is translational and rotational movement.
- K translational = ½ mv2
- K rotational = ½ I ⍵2
- Total kinetic energy is the sum of translational and rotational kinetic energy.
- When comparing objects with different Moments of Inertia, consider how it impacts Rotational Kinetic Energy.
- Higher I results in higher KEr.
Angular Momentum, Impulse, and Conservation of Angular Momentum
- For a point object traveling linearly towards an object before collision, angular momentum can be translated with L= mvR.
- This accounts for substituting with v=⍵r or ⍵ = v/R and I = mR2.
- Example: L =I ⍵ = mR2 * v/R = mvR
- Linear momentum is conserved if the collided object is free to move.
- Angular momentum is conserved if the collided object is free to move around an axis.
- If either condition is limited, one or both momentums will not be conserved.
- Kinetic energy is not conserved in inelastic collisions, KE before collision will be greater than KE after.
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