# An object with a mass of # 2 kg# is traveling in a circular path of a radius of #4 m#. If the object's angular velocity changes from # 4 Hz# to # 8 Hz# in # 3 s#, what torque was applied to the object?

The torque was

The torque is the rate of change of angular momentum

The rate of change of angular velocity is

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Torque = Moment of Inertia * Angular Acceleration Angular Acceleration = (Final Angular Velocity - Initial Angular Velocity) / Time

Angular Acceleration = (8 Hz - 4 Hz) / 3 s Angular Acceleration = 1.33 Hz/s

Moment of Inertia (for a point mass rotating about an axis at a distance r) = mass * radius^2 Moment of Inertia = 2 kg * (4 m)^2 = 32 kg*m^2

Torque = 32 kg*m^2 * 1.33 Hz/s = 42.56 N*m

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A solid disk with a radius of #5 m# and mass of #4 kg# is rotating on a frictionless surface. If #3 W# of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at #4 Hz#?
- A solid disk, spinning counter-clockwise, has a mass of #4 kg# and a radius of #3 m#. If a point on the edge of the disk is moving at #2/5 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?
- An object with a mass of # 2 kg# is traveling in a circular path of a radius of #7 m#. If the object's angular velocity changes from # 7 Hz# to # 9 Hz# in # 3 s#, what torque was applied to the object?
- A solid disk with a radius of #3 m# and mass of #12 kg# is rotating on a frictionless surface. If #480 W# of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at #4 Hz#?
- A solid disk with a radius of #5 m# and mass of #4 kg# is rotating on a frictionless surface. If #15 W# of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at #5 Hz#?

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