need some help, A ball with an initial angular velocity of 20.0 rads /s and a rotational inertia of 0.4kgm rolls uphill with an acceleration of -4.00 rad/s . Calculate the net torque acting on the ball. Calculate the angular displacement after 5.00 s.
To calculate the net torque acting on the ball, we can use Newton's second law for rotational motion, which states that the torque is equal to the product of the moment of inertia and the angular acceleration.
The formula for torque is given by:
Torque = Moment of Inertia * Angular Acceleration
Substituting the given values:
Torque = (0.4 kgm) * (-4.00 rad/s^2)
= -1.6 kgm^2/s^2
Therefore, the net torque acting on the ball is -1.6 kgm^2/s^2.
To calculate the angular displacement after 5.00 s, we can use the formula for angular displacement:
Angular Displacement = (Initial Angular Velocity * Time) + (0.5 * Angular Acceleration * Time^2)
Substituting the given values:
Angular Displacement = (20.0 rad/s * 5.00 s) + (0.5 * -4.00 rad/s^2 * (5.00 s)^2)
= 100 rad - 50 rad
= 50 rad
Therefore, the angular displacement after 5.00 s is 50 rad.