Torque and Rotational Motion FlinnPREP

30 ω

A torque of 15 N•m is applied to a disk of radius 1.5 m starting from rest until it reaches an angular velocity of 4 rad/s. What power was applied? (The formula for the moment of inertia for a solid cylinder or disk around an axis along the cylinder's axis is 1/2 MR2, where M is the cylinder's mass and R is its radius.)

23 rad/s

A wheel rolling without slipping with angular velocity of 3 rad/s is accelerated linearly at 5 m/s2 for 2 seconds. If the radius of the wheel is 0.5 m, what is the new angular velocity?

The angular acceleration

An increase in net torque causes which of the following to increase?

1.5 rad

An object is rotating through 180 degrees every 2.1 seconds. What is its angular velocity?

100 J

An object with moment of inertia 8 kg•m2 and mass 2 kg is spinning at 5 rad/s. What is its rotational kinetic energy?

(Yes) because (the component of the force parallel to the moment arm from the center of mass will cause translational acceleration and the component perpendicular will cause torque)

Can force be applied in a rotational and translational way simultaneously?

Counterclockwise

Consider a person sitting on a freely rotating platform. If the person then rotates the wheel to their left. Which way does the chair rotate when viewed from above?

It increases because the moment of inertia increases.

If the radius of a spinning object increases while keeping the mass and angular speed constant, what happens to the object's kinetic energy?

The system's acceleration will: (decrease) because (the moment of inertia of the pulley increases which decreases its angular acceleration)

If two masses with different weights hang on opposite sides of a pulley, the system will accelerate whether or not the pulley has mass. If the mass of the pulley is increased without changing its radius, what will be the effect on the systems acceleration? Why?

Farther, the linear velocity is higher

If you want to experience a faster ride, should you sit closer or farther from the center on a spinning swing ride?

They rotate clockwise as a system

Imagine an ice skater is spinning clockwise very quickly and a friend comes up and grabs the skater. Assume the ice is frictionless, what happens to the pair?

Object B

Object A rotates with an angular velocity of 3 rad/s; object B at 180 degrees/s. Which is rotating faster?

The door moves toward: (Person B) because (the torque from person A is greater)

Person A pushes a door at 0.3 m from the hinge with a force of 9 N. Person B pushes from the other side at 0.25 m from the hinge with a force of 10 N. Who does the door move toward?

They reach the goalie in the same amount of time because B's extra energy is only in rotation and doesn't contribute to the translational motion.

Soccer player A kicks a ball at the goalie. Soccer player B kicks a ball from the same starting place in exactly the same way except she adds an additional force that adds spin to the ball. Which ball will reach the goalie in less time and why?

The object with the highest moment of inertia is the: (hoop) because (the mass is concentrated at a larger distance)

There are three objects with equal mass m and equal radius r. A solid sphere, a spherical shell and a hoop. Which has the highest moment of inertia around the axis shown and why?

The center of mass is: (2.6) m from the (right)

Three men stand on a board. The board is massless and 5.0 m long. Man A stands at 0.9 m from the left edge and has a mass of 80 kg, Man B stands at 2.1 m from the left edge and has a mass of 70 kg, and Man C stands at 3.9 m from the left edge and has a mass of 100 kg. Where is the center of mass of the system?

3.0 m/s

A spherical shell with radius 0.4 m and mass 2 kg is rotated from rest by 6 J of work. What is the velocity of a point on the shell around its fixed center? (The formula for the moment for a thin spherical shell around an axis through its center is 2/3 MR2, where M is the shell's mass and R is its radius.)

When the skater bends, the angular velocity: (slows down) and when he extends his arms, it (slows down)

A spinning figure skater with tucked arms first bends at the waist by 90 degrees then after some time extends his arms. What happens to the skaters angular velocity at each change of position?

14 rad/s

A thin spherical shell with mass 4 kg and radius 0.7 m is moving at 8 m/s, not rotating, when it reaches a region where the surface is made of massless rollers. The friction between the sphere and the rollers is static such that the sphere starts rolling and stops moving linearly. What is the final angular velocity of the sphere?

Upward

A top spins on a table. Looking from the top, it's spinning counterclockwise. In which direction does the angular velocity vector point?

0.8 N*m

A sphere with a mass of 2 kg and radius 50 cm is rotated around its center with an acceleration of 4 rad/s2. What net torque is causing the acceleration? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius)

The angular momentum is: (3.2) kg·m2/s, and it points (counterclockwise)

A 1.5 kg steel sphere is attached to one end of a 0.8 meter massless rod. A 4.0 kg steel sphere is attached to one end of a separate but identical rod. The free end of each rod is fixed to the same point and both spheres are set into motion with an angular speed of 2 rad/s. The 1.5 kg sphere rotates clockwise (when viewed from above); and the 4.0 kg sphere rotates counterclockwise (when viewed from above). What is the angular momentum of the system, and in which direction does it point?

12.5 rad/s

A car with four wheels moves forward at 5 m/s. If each wheel's radius is 0.4 m, what is the angular velocity of each wheel?

Angular velocity down and angular momentum down

A disc is spinning clockwise as viewed from above. What are the directions of the resulting angular velocity and the angular momentum?

The work done is: (80) m/s2 , with units of (J)

A disk's circumference is 3 m, and a point on the edge spins three times with a tangential acceleration of 4 m/s2. If the disk has a mass of 5 kg, what is the work done? (The formula for the moment of inertia for a disk is 1/2 MR2, where M is the cylinder's mass and R is its radius.)

(rotational acceleration) ; (linear acceleration)

A force is applied to a system at a point away from the center of mass. Assuming the system is not fixed in place, which TWO of the following will change? (TWO answers)

The wheel does not spin because the lever arm associated with the force is zero.

A force is applied to a wheel at rest. The force is perpendicular to the wheel's axis of rotation at the axis of rotation. What happens?

The torque is: (1.1) (N*m)

A force of 4 N is applied to the edge of a wheel at an angle of 30 degrees from perpendicular to the radius of a wheel. The wheel's circumference is 2 m. What is the torque applied?

0.87 N*m

A force of 5 N is applied at a distance 0.2 m from the point of rotation at an angle of 60 degrees between the force and the ray from the point of rotation to the location where the force is applied. What is the torque applied?

It must withstand: (3920) (N*m)

A man stands at the end of a 5-m horizontal beam fixed at the opposite end to a wall. Using the beam fastener as the axis of rotation, what torque does the man exert on the beam if the man has a mass of 80 kg? (You may assume the beam does not rotate.)

7 cm

A massless barbell is 2 m long. There is 90 kg weight 8 cm from one edge and a 110 kg weight 12 cm from the other edge. How far from the center of the bar is the center of mass?

3.8 kg*m^2

A massless figure skater with arms 0.7 m long holds two masses in opposite directions. 5 kg is 45 degrees up from parallel to the ground to the skater's left, the other is 7 kg positioned 30 degrees down from parallel to the skater's right. What is the moment of inertia around a vertical axis through the middle of the skater?

The moment of inertia is: 6.8 (kg·m^2)

A massless rod 3 m long has a solid sphere, with a mass of 3 kg and radius of 0.1 m, glued to its middle. The rod rotates around one end (like a clock hand), but the sphere does not. What is the moment of inertia of this system around the fixed end of the rod? (The formula for moment of inertia of a sphere around an axis through its center is 2/5 MR2 and the formula for inertia of a long thin stick around one end is 1/2 ML2 where M and L are the mass and the length of the stick respectively.)

22.4 J

A solid sphere of mass 2 kg rolls at a speed of 4 m/s. The radius is 0.5 m. What is the total kinetic energy? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius.)

71%

A solid sphere of mass 5 kg rolls at a speed of 2 m/s. The radius is 0.5 m. What percentage of of the total kinetic energy is translational kinetic energy? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius.)

The total kinetic energy is: (39.2) J; the rotational kinetic energy is (11.2) J

A solid sphere of radius 20 cm and mass 2 kg rolls down an incline from a height of 2 m where it was initially at rest. What is the total kinetic energy and rotational kinetic energy at the bottom of the ramp? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius.)

Object B

Three objects all have radius r. Object A is a solid sphere of mass 4 kg, object B is a thin spherical shell of mass 2 kg, and object C is a solid cylinder of mass 3 kg. Which object has the smallest moment of inertia? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius. The formula for the moment of inertia for a solid cylinder or disk around an axis along the cylinder's axis is 1/2 MR2, where M is the cylinder's mass and R is its radius. The formula for the moment for a thin spherical shell around an axis through its center is 1/2 MR2, where M is the shell's mass and R is its radius.)

False, they do not have the same basic units.

True or false? Work and torque have the same units; therefore, they measure the same thing.

30 rad/s

Two gears rotate, one of radius 0.3 m and the other 0.1 m. The larger gear rotates at 10 rad/s, moving the smaller gear. What is the angular velocity of the smaller gear?

θ, ω, α

What are the angular quantities that correspond to the linear quantities of (in order) position, velocity and acceleration?

16 kg•m^2/s

What is the change in angular momentum if a torque of 8 N•m is applied for 2 seconds?

There is no external force

When a spinning skater pulls his arms in and speeds up, what external force is causing the acceleration?

The angular velocity is: (25 rad/s); the system's energy is (Yes, increased)

You are making pottery, and you start to spin the pottery wheel. You create an angular acceleration of 5 rad/s2. What is the angular velocity after 5 seconds? Have you changed the energy of the system and if so, how?

The kinetic energy is: (40) (J)

You roll a bowling ball with a radius of 15 cm and mass 8 kg down the bowling lane at 5 m/s. What is the rotational kinetic energy of the ball? (The formula for the moment of inertia for a solid sphere around an axis through its center is 2/5 MR2, where M is the sphere's mass and R is its radius.)