A 0.30-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 3.0 rad/s² over a 5.0-s interval? A) 12 rad B) 25 rad C) 37 rad D) 0.50 rad

Question

Quizplus · Accepted Answer

The initial angular velocity is zero, and the constant angular acceleration is 3.0 rad/s^2. Using the equation:

θ = ω_i*t + (1/2)*α*t^2

where θ is the total angular displacement, ω_i is the initial angular velocity, α is the angular acceleration, and t is the time interval, we can calculate the total angular displacement:

θ = (0)*5.0 + (1/2)*(3.0)*(5.0)^2 = 37.5 rad

However, this is the total displacement, so we need to subtract the initial angle (which is zero) to get the net angular displacement:

θ_net = 37.5 rad - 0 rad = 37.5 rad

Therefore, the tire rotates 37.5 radians during the 5.0-second interval, which is closest to choice C, 37 rad.

A 030-M Radius Automobile Tire Rotates How Many Rad After Starting