A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$is in radians, c = 1.0 rad/s, and d = -0.50 rad/s³. At t = 2.0 s the magnitude of the tangential acceleration of an object placed 10.0 cm from the center of the wheel is A) -0.60 m/s². B) -0.30 m/s². C) 0 m/s². D) 0.30 m/s².

Question

Quizplus · Accepted Answer

Explanation:The tangential acceleration is given by:$$a_t = r \alpha = r \frac{d^2 \phi}{dt^2} = r (2d t)$$At t = 2.0 s,$$a_t = (0.100 	ext{ m})(2)(-0.50 	ext{ rad/s}^3)(2.0 	ext{ s})^2 = -0.60 	ext{ m/s}^2$$

A Wheel Undergoes Rotational Motion According to the Equation ϕ(rad)=ct+dt3\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }ϕ(rad)=ct+dt3

A Wheel Undergoes Rotational Motion According to the Equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$