Final answer:
The point's angular position at t=0 is 0 radians, and its angular velocity at t=0 is also 0 rad/s. The point's angular velocity at t=4s and its angular acceleration at t=2s can be calculated using the first and second derivatives of the angular position, respectively. The angular acceleration is not constant, as it changes with time.
Step-by-step explanation:
The angular position given for a rotating wheel is θ = 5t3 - 2t3, where θ is in radians and t is in seconds. This information allows us to solve for various properties of rotational motion such as angular position, angular velocity, and angular acceleration.
For t = 0:
- Angular Position: Plugging t = 0 into the equation, we get θ = 0 radians.
- Angular Velocity: The first derivative of θ with respect to time (t) gives angular velocity (ω = dθ/dt). At t = 0, the angular velocity is 0 rad/s since the derivative of the constant and cubic term are zero when t = 0.
At t = 4 seconds:
- The angular velocity is found by taking the first derivative of θ with respect to t, which gives ω = 15t2 - 6t2, and evaluating it at t = 4 s.
At t = 2 seconds:
- The angular acceleration (α) is the second derivative of θ with respect to t, which can be calculated and evaluated at t = 2 s.
Angular Acceleration Constancy:
- Angular acceleration is not constant as it depends on time t and is given by the second derivative of θ (α = d2θ/dt2).