A large playground turntable of radius starts from rest and rotates with a constant…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A large playground turntable of radius 2.0m starts from rest and rotates with a constant angular acceleration. A painted dot on the rim is observed to move 1.6m along the circular path in the first 1.0s.
A physics class wishes to compare this motion to a toy car that accelerates linearly from rest with the same magnitude of constant acceleration such that both the dot and the car have identical tangential (linear) speeds at every instant.
Provide complete solutions to the following parts; use algebraic symbols first and insert numerical values only in the final step of each calculation.
(a) Derive an algebraic expression for the angular acceleration α of the turntable in terms of the given arc length s, radius r, and time t.
(b) Using your expression, calculate the numerical value of α.
(c) Determine the linear acceleration of the toy car so that its motion matches the tangential motion of the painted dot at all times.
(d) After 3.0s, how far has the toy car traveled? State any assumptions clearly.