A large turntable starts from rest and rotates with a constant angular acceleration of

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

\alpha = 0.60\,\text{rad}\,\text{s}^{-2}

. Two identical sensors are mounted at fixed distances from the axis: sensor X at

r_X = 0.15\,\text{m}

and sensor Y at

r_Y = 0.50\,\text{m}

. The sensors measure tangential acceleration of the material directly beneath them. (a) After

t = 4.0\,\text{s}

of rotation, what is the angular speed of the turntable? (b) At that same instant, what tangential acceleration does each sensor record? (c) Compute the ratio

a_{t,Y}/a_{t,X}

and explain, based on your results, whether the ratio depends on the elapsed time. (d) Determine the linear speed of sensor Y at

t = 4.0\,\text{s}

. Show your work and include units.

Related theory

Linear-Rotational Mapping
Rotational Kinematics
Angular acceleration

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