2018 #3 Free Response Question - AP Physics 1 - Exam Solution

A disk initially spins with a positive angular velocity ω₀ and comes to rest at time t₁. If friction exerts a constant torque, which graph best represents the disk's angular velocity as a function of time?

• A graph starting at ω₀ and linearly decreasing to 0 at t₁.

• A graph starting at ω₀ and exponentially decreasing to 0 at t₁.

• A graph starting at 0 and linearly increasing to ω₀ at t₁.

• A graph starting at ω₀ and remaining constant until t₁, then dropping to 0.

A disk initially spins with a positive angular velocity and comes to rest due to a constant frictional torque. Which graph best represents the disk's angular acceleration as a function of time?

• A horizontal line above the x-axis.

• A horizontal line below the x-axis.

• A linearly decreasing line starting above the x-axis.

• A linearly increasing line starting below the x-axis.

Which equation correctly relates the net torque (Στ) acting on a rotating object to its rotational inertia (I) and angular acceleration (α)?

• Στ = I/α

• Στ = Iα

• Στ = α/I

• Στ = I + α

For a disk with initial angular velocity ω₀ that comes to rest at time t₁ due to a constant frictional torque τ₀, what is the expression for its rotational inertia (I)?

• I = τ₀ω₀/t₁

• I = ω₀t₁/τ₀

• I = τ₀t₁/ω₀

• I = τ₀/(ω₀t₁)

When oil is applied to the contact surface between the axle and the disk, what is the immediate effect on the system?

• The rotational inertia of the disk increases.

• The net torque acting on the disk increases.

• The friction between the axle and the disk decreases.

• The angular velocity of the disk instantly becomes zero.

A disk initially rotates with a positive angular velocity. At a certain time, oil is applied to the axle, gradually reducing friction. How does the disk's angular acceleration change after the oil is applied?

• It remains constant at its initial negative value.

• It becomes zero immediately and stays zero.

• Its magnitude gradually decreases, approaching zero.

• Its magnitude gradually increases, moving further away from zero.

A disk initially rotates with a positive angular velocity. At a certain time, oil is applied to the axle, gradually reducing friction. How does the disk's angular velocity change after the oil is applied?

• It continues to decrease linearly until it stops.

• It decreases at a slower rate, with the rate of decrease gradually diminishing.

• It immediately stops decreasing and maintains a constant positive angular velocity.

• It begins to increase as the friction is reduced.

Two equations are proposed to model the magnitude of torque (τ) exerted by the axle on a disk after oil is applied, where t is time and t₁ is a constant. 1. τ₁ = C₁ (t - 0.5 t₁) 2. τ₂ = C₂ / (t + 0.5 t₁) Which equation better models the experiment, given that the torque magnitude should start at a positive value when oil is first applied (t = 0.5 t₁) and then decrease as more oil spreads?

• Equation 1, because it shows torque increasing over time.

• Equation 1, because it shows torque starting at zero and increasing.

• Equation 2, because it shows torque starting at a positive value and decreasing over time.

• Equation 2, because it shows torque starting at zero and decreasing over time.