At time t=0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 35.0 rad/s2 until a circuit breaker trips at time t= 2.50 s. From then on, the wheel turns through an angle of 440 rad as it coasts to a stop at constant angular deceleration.
a) Through what total angle did the wheel turn between t= 0 and the time it stopped? answer in rad
b) At what time does the wheel stop? (secs)
c)What was the wheel’s angular acceleration as it slowed down?
Express your answer in radians per second per second.
♦ Relevant knowledgeThe body is moving in a circular loop and the speed of the body changes from its starting location to its closing position over a period of time is referred to as angular (or rotational acceleration). It needs the magnitude and direction to determine their actions.
This problem can be solved using rotational kinematic equations.
Initially, determine the angular displacement. Later, determine the angular velocity.
Find the angular acceleration.
This is the expression for the angular displacement of rotational kinematics equations:
θ1=ω0t+1⁄2 at2
Here, ω0 is initial angular speed, t is the time, α is the angular acceleration.
This is the expression for the angular speed of the wheel:
ω=ω0+αt
Here, ω0
The expression for the angular acceleration is:
α‘= (ω‘–ω) ⁄ Δt
Here, ω‘ is the angular velocity when the wheel stops and Δt is change in the time.