Physics, 07.03.2020 05:05 pgjohnston001
Learning Goal:
To understand work and power in rotational systems and to use the work-energy theorem to determine kinematics variables.
The variables used in standard linear mechanics (the study of objects that do not rotate) all have analogues in rotational mechanics (the study of objects that rotate). Here is a summary of variables used in kinematics and dynamics.
Linear variable Rotational variable
linear position: x angular position: θ
linear velocity: v angular velocity: ω
linear acceleration: a angular acceleration: α
linear inertia (mass): m moment of inertia: I
force: F torque: Ï„
The kinetic energy Krot associated with a rotating object is defined as
Krot=12Iω2,
where ω is measured in rad/s. Applying a torque can change the angular velocity of an object, and hence its kinetic energy. The torque is said to have done work on the object, just as a force applied over a distance can change the kinetic energy of an object in linear mechanics. In terms of rotational variables, the work W done by a constant torque τ is
W=τΔθ,
where Δθ describes the total angle, measured in radians, through which the object rotates while the torque is being applied.
Consider a motor that exerts a constant torque of 25.0 Nâ‹…m to a horizontal platform whose moment of inertia is 50.0 kgâ‹…m2. Assume that the platform is initially at rest and the torque is applied for 12.0 rotations. Neglect friction.
Part A
How much work W does the motor do on the platform during this process?
Enter your answer in joules to four significant figures.
Answers: 1
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Learning Goal:
To understand work and power in rotational systems and to use the work-en...
To understand work and power in rotational systems and to use the work-en...
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