A Merry Go Round (MGR) has a radius of 18 meters. At t = 0, the Merry Go Round (MGR) has an angular velocity of 1.2 radians/second. The MGR also has a constant angular acceleration. After 3 seconds have elapsed, MGR has an angular velocity of 2.5 radians/second. A RIDER IS STANDING AT THE OUTER EDGE OF THE MGR.(a) What is the angular acceleration of the MGR? 0.433 radians/s^2(b) What is the tangential acceleration of the MGR? m/s^2(c) What is the tangential velocity of the RIDER after 3 s?
Question
A Merry Go Round (MGR) has a radius of 18 meters. At t = 0, the Merry Go Round (MGR) has an angular velocity of 1.2 radians/second. The MGR also has a constant angular acceleration. After 3 seconds have elapsed, MGR has an angular velocity of 2.5 radians/second. A RIDER IS STANDING AT THE OUTER EDGE OF THE MGR.(a) What is the angular acceleration of the MGR? 0.433 radians/s^2(b) What is the tangential acceleration of the MGR? m/s^2(c) What is the tangential velocity of the RIDER after 3 s?
Solution
(a) The angular acceleration (α) can be calculated using the formula α = (ωf - ωi) / t, where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time. In this case, ωf = 2.5 rad/s, ωi = 1.2 rad/s, and t = 3 s. So, α = (2.5 - 1.2) / 3 = 0.433 rad/s^2.
(b) The tangential acceleration (a_t) can be calculated using the formula a_t = r * α, where r is the radius and α is the angular acceleration. In this case, r = 18 m and α = 0.433 rad/s^2. So, a_t = 18 * 0.433 = 7.794 m/s^2.
(c) The tangential velocity (v_t) can be calculated using the formula v_t = r * ω, where r is the radius and ω is the angular velocity. After 3 seconds, the angular velocity is 2.5 rad/s. So, v_t = 18 * 2.5 = 45 m/s. Therefore, the tangential velocity of the rider after 3 seconds is 45 m/s.
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