Connecting Linear and Rotational Motion AP Physics 1 FRQ – Exam Style Questions etc.
Connecting Linear and Rotational MotionAP Physics 1 FRQ
Unit 5: Torque and Rotational Dynamics
Weightage : 10-15%
Exam Style Practice Questions, Connecting Linear and Rotational Motion AP Physics 1 FRQ
Question
A ball of mass m is attached by two strings to a vertical rod. as shown above. The entire system rotates at constant angular velocity ω about the axis of the rod.
a. Assuming ω is large enough to keep both strings taut, find the force each string exerts on the ball in terms of ω, m, g, R, and θ.
b. Find the minimum angular velocity, ωmin for which the lower string barely remains taut.
▶️Answer/Explanation
Ans:
a. Define a coordinate system with the x-axis directed to the vertical rod and the y-axis directed upwards and perpendicular to the first. Let T1 be the tension in the horizontal string. Let T2 be the tension in the string tilted upwards.
Applying Newton’s Second Law: \(\sum F_{x}\) = T1 + T2 sin θ = mω2R; \(\sum F_{y}\) = T2 cos θ – mg = 0
Solving yields: T2 = mg/cos θ and T1 = m(ω2R – g tan θ)
b. Let T1 = 0 and solving for ω gives ω = (g tanθ/R)1/2