When can kinematic equations of motion for rotational motion be used
Added by Rodney E.
Step 1
- Confirm the motion is rotational (an object or a point moves around an axis). - Define angular variables: theta = angular displacement, omega = angular velocity, alpha = angular acceleration. Use theta0 and omega0 for initial values and t for time. Show more…
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In describing rotational motion it is often useful to develop an analogy with translational motion. First, write a set of equations describing translational motion. Then write the rotational analogs (for example, $\theta=\theta 0 \ldots$ $\theta=\theta_{0} \ldots$ of the translational equations (for example, $\mathrm{x}=\mathrm{x} 0+\mathrm{v} 0 \mathrm{xt}+12 \mathrm{axt} 2$ $x=x_{0}+v_{0 x} t+\frac{1}{2} a_{x} t^{2}$ ) using the following legend: $\mathrm{x} \Leftrightarrow \theta \mathrm{v} \mathrm{x} \Leftrightarrow \omega \mathrm{zax} \Leftrightarrow \alpha \mathrm{z} \mathrm{Fx} \Leftrightarrow \mathrm{tzm} \Leftrightarrow \operatorname{Ipx} \Leftrightarrow$ LzKtranslational $\Leftrightarrow$ Krotational $x \Leftrightarrow \theta \quad v_{x} \Leftrightarrow \omega_{z} \quad a_{x} \Leftrightarrow \alpha_{z} \quad F_{x} \Leftrightarrow \tau_{z} \quad m \Leftrightarrow I$ $$ p_{x} \Leftrightarrow L_{z} \quad K_{\text {translational }} \Leftrightarrow K_{\text {rotational }} $$
The kinematic equations for rotational motion are valid for constant angular acceleration, changing angular acceleration, constant angular velocity, and changing angular velocity. By convention, a torque which has a tendency to cause a counter-clockwise rotation is said to be positive, while a torque which has a tendency to cause a clockwise rotation is said to be negative. The equation Iω best describes the angular momentum for a rotating object about a fixed axis. If the angular acceleration is nonzero and constant, the object must be steadily increasing or decreasing its angular velocity. For an object to be in rotational equilibrium, the net torque must be equal to zero. If a constant net torque is applied to an object with a fixed axis, the object will experience a constant angular acceleration resulting in a changing angular velocity.
Jeff V.
Just as every linear motion equation has an equivalent rotational motion equation, every linear motion Kinematics problem has an equivalent rotational motion Kinematics problem too. If the linear motion problem is “A car initially has a velocity of 10 m/s and it accelerates at 3.0 m/s2. Determine the time it takes the car to travel 200 m. ” then 1) Write the equivalent rotational motion problem. 2) Draw the detailed sketch of the rotational motion problem. 3) Write the rotational motion Kinematics equations with the correct numbers placed into the equations. 4) Use the rotational equivalent numbers for 10m/s, 3.0 m/s2 and 200 m and then solve for the time of the rotational motion problem that you wrote.
Stephen Z.
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