A bicycle wheel of radius is rigidly attached to a frame so that it can rotate freely…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A bicycle wheel of radius 0.35m is rigidly attached to a frame so that it can rotate freely about its central axle in a horizontal plane. Two small reflective markers are glued to the rim: Marker P is located at the top of the wheel, and Marker Q is located at the midpoint of one of the spokes at a radial distance of 0.18m from the axle. At the instant shown, the wheel has a counter-clockwise angular acceleration. Assume the markers remain fixed relative to the wheel.
Answer the following questions about the motion of the two markers. Express any numerical answers with appropriate units.
(a) Describe qualitatively how the tangential accelerations of Markers P and Q compare at that instant. Include an explanation based on their positions on the wheel.
(b) Suppose the angular acceleration of the wheel increases linearly with time according to α(t)=kt, where k is a positive constant. Derive an expression for the ratio at,P/at,Q as a function of time, where at,P and at,Q are the magnitudes of the tangential accelerations of Markers P and Q, respectively.
(c) If k=3.0rad/s3, calculate the numerical value of the ratio at,P/at,Q at t=2.0s. Show all work clearly.