How do you calculate torque?

Identify the force applied. 2. Determine the distance from the axis of rotation to the point where the force is applied (lever arm). 3. Calculate torque using the formula $\tau = rF\sin\theta$ , where $\theta$ is the angle between the force and the lever arm.

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How do you calculate torque?

Identify the force applied. 2. Determine the distance from the axis of rotation to the point where the force is applied (lever arm). 3. Calculate torque using the formula $\tau = rF\sin\theta$ , where $\theta$ is the angle between the force and the lever arm.

How do you determine angular acceleration using Newton's Second Law for Rotation?

Calculate the net torque ( $Sigma \tau$ ) acting on the object. 2. Determine the rotational inertia (I) of the object. 3. Apply the formula $\alpha = \frac{\Sigma \tau}{I}$ to find the angular acceleration.

What steps are involved in analyzing a system with both linear and rotational motion?

Perform a linear analysis to determine the linear acceleration of the center of mass using $\Sigma \vec{F} = m\vec{a}$ . 2. Perform a rotational analysis to determine the angular acceleration about the axis of rotation using $\Sigma \tau = I\alpha$ . 3. Relate linear and angular quantities if necessary (e.g., for rolling without slipping, a = rα).

How do you calculate net torque?

Add up all the individual torques acting on the object as vectors. $\sum \tau = \tau_1 + \tau_2 + ...$

How do you calculate rotational inertia for a system of point masses?

Use the formula: $I = \sum mr^2$ , where m is the mass of each point and r is its distance from the axis of rotation.

How do you relate linear and angular speed for rolling without slipping?

The linear speed of the center of mass is related to the angular speed by $v_{cm} = R\omega$ , where R is the radius of the object.

How do you determine the direction of angular acceleration?

The direction of the angular acceleration is the same as the direction of the net torque vector. Clockwise torque results in clockwise angular acceleration, and counterclockwise torque results in counterclockwise angular acceleration.

What is the first step in solving rotational dynamics problems?

Draw a free body diagram showing all forces acting on the object and their points of application.

Compare and contrast torque and force.

Torque: Rotational force, causes rotation. | Force: Linear force, causes linear acceleration.

Compare and contrast rotational inertia and mass.

Rotational Inertia: Resistance to changes in rotational motion, depends on mass distribution. | Mass: Resistance to changes in linear motion.

Compare and contrast tangential speed and angular speed.

Tangential Speed: Linear speed of a point on a rotating object. | Angular Speed: Rate of change of angular displacement.

Compare the rotational inertia of a solid cylinder and a hollow cylinder of the same mass and radius.

Solid Cylinder: Lower rotational inertia, mass closer to the axis of rotation. | Hollow Cylinder: Higher rotational inertia, mass farther from the axis of rotation.

Compare clockwise and counterclockwise torque.

Clockwise Torque: Causes clockwise angular acceleration. | Counterclockwise Torque: Causes counterclockwise angular acceleration.

All Flashcards

How do you calculate torque?

Identify the force applied. 2. Determine the distance from the axis of rotation to the point where the force is applied (lever arm). 3. Calculate torque using the formula $\tau = rF\sin\theta$ , where $\theta$ is the angle between the force and the lever arm.

How do you determine angular acceleration using Newton's Second Law for Rotation?

Calculate the net torque ( $Sigma \tau$ ) acting on the object. 2. Determine the rotational inertia (I) of the object. 3. Apply the formula $\alpha = \frac{\Sigma \tau}{I}$ to find the angular acceleration.

What steps are involved in analyzing a system with both linear and rotational motion?

Perform a linear analysis to determine the linear acceleration of the center of mass using $\Sigma \vec{F} = m\vec{a}$ . 2. Perform a rotational analysis to determine the angular acceleration about the axis of rotation using $\Sigma \tau = I\alpha$ . 3. Relate linear and angular quantities if necessary (e.g., for rolling without slipping, a = rα).

How do you calculate net torque?

Add up all the individual torques acting on the object as vectors. $\sum \tau = \tau_1 + \tau_2 + ...$

How do you calculate rotational inertia for a system of point masses?

Use the formula: $I = \sum mr^2$ , where m is the mass of each point and r is its distance from the axis of rotation.

How do you relate linear and angular speed for rolling without slipping?

The linear speed of the center of mass is related to the angular speed by $v_{cm} = R\omega$ , where R is the radius of the object.

How do you determine the direction of angular acceleration?

What is the first step in solving rotational dynamics problems?

Draw a free body diagram showing all forces acting on the object and their points of application.

Compare and contrast torque and force.

Torque: Rotational force, causes rotation. | Force: Linear force, causes linear acceleration.

Compare and contrast rotational inertia and mass.

Rotational Inertia: Resistance to changes in rotational motion, depends on mass distribution. | Mass: Resistance to changes in linear motion.

Compare and contrast tangential speed and angular speed.

Tangential Speed: Linear speed of a point on a rotating object. | Angular Speed: Rate of change of angular displacement.

Compare the rotational inertia of a solid cylinder and a hollow cylinder of the same mass and radius.

Solid Cylinder: Lower rotational inertia, mass closer to the axis of rotation. | Hollow Cylinder: Higher rotational inertia, mass farther from the axis of rotation.

Compare clockwise and counterclockwise torque.

Clockwise Torque: Causes clockwise angular acceleration. | Counterclockwise Torque: Causes counterclockwise angular acceleration.