Final answer:
The magnitude of the tangential velocity of the point on a disk rim, after turning through 3.1 revolutions with a constant force applied at an angle, can be found using the tangential force to calculate torque, then angular acceleration, followed by angular velocity, and ultimately the tangential velocity by multiplying the radius with angular velocity.
Step-by-step explanation:
The problem describes a scenario involving a typical rotational dynamics and energy conservation situation. To find the tangential velocity of a point on the rim of the disk after 3.1 revolutions, we need to calculate the angular displacement, angular velocity, and finally convert that to tangential velocity. Since the applied force is not tangential, only a component of it will lead to the rotation of the disk.
The tangential component of the force (Ft) can be found using trigonometry: Ft = F * cos(35 degrees). The torque (τ) due to this force is the product of the tangential force and the radius (r): τ = r * Ft. With torque, we can find angular acceleration (α) using the relation τ = Iα, where I is the moment of inertia of the disk (I = 0.5 * m * r2 for a uniform disk).
The disk turns through 3.1 revolutions, which is θ = 3.1 * 2π radians. Using the kinematic equation θ = 0.5αt2, we can solve for time (t) and then use ω = αt to find the angular velocity (ω). Finally, the tangential velocity of a point on the rim is v = rω.