PhysicsBowl 2018 Q20

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PhysicsBowl 2018

20) This question requires us to use rotational motion to solve for the angular acceleration of the pulley. Let's first start with a free body diagram of the situation.

Where τ is torque, T is tension, m is mass of the block, and g is acceleration due to gravity

From this point, we can set up Newton's second law for net force and an equation for net torque.

Where τ is torque, I is moment of inertia, α is angular acceleration, T is tension, m is mass of the block, a[net] is the net acceleration, and g is acceleration due to gravity

We can substitute I with the moment of inertia predefined formula for a disk, τ[T] with r x T (the cross-product of radius and tension), and a[net] with its angular acceleration relation.

Where τ is torque, I is moment of inertia, α is angular acceleration, m is the mass of the block, a[net] is the net acceleration of the block, g is the acceleration due to gravity, T is tension, M is the mass of the pulley, and R is the radius of the pulley

We have a system of 2 equations with two unknown values: T(tension) and α(angular acceleration). We can solve for α and then plug in our given values.

Where α is angular acceleration, m is the mass of the block, a[net] is the net acceleration of the block, g is the acceleration due to gravity, M is the mass of the pulley, and R is the radius of the pulley

Answer: A