Question

In: Physics

A grinding wheel is initially rotating with an angular velocity 4000 rad/s when its motor is...

A grinding wheel is initially rotating with an angular velocity 4000 rad/s when its motor is suddenly turned off. It comes to rest in 10 s. Through what angle did it rotate during the first second after the motor was turned off?

Please show work and Express answer in radians.

Thank you!

Solutions

Expert Solution

Initial angular velocity of the grinding wheel = 1 = 4000 rad/s

Final angular velocity of the grinding wheel = 2 = 0 rad/s (Comes to rest)

Time taken by the grinding wheel to come to rest = T = 10 sec

Angular acceleration of the grinding wheel =

2 = 1 + T

0 = 4000 + (10)

= -400 rad/s2

Negative as it is deceleration.

Angle through which the grinding wheel rotates in the first second =

Time period = T1 = 1 sec

= 1T1 + T12/2

= (4000)(1) + (-400)(1)2/2

= 3800 rad

Angle through which the grinding wheel rotates in the first second = 3800 rad


Related Solutions

A Wheel initially rotating at an angular velocity of 15.0 rad/s is decelerating at a rate...
A Wheel initially rotating at an angular velocity of 15.0 rad/s is decelerating at a rate of 2.0 rad/s². How many revolutions will the wheel make before coming to rest?
At time t=0 a grinding wheel has an angular velocity of 29.0 rad/s . It has...
At time t=0 a grinding wheel has an angular velocity of 29.0 rad/s . It has a constant angular acceleration of 29.0 rad/s2 until a circuit breaker trips at time t = 2.30 s . From then on, the wheel turns through an angle of 433 rad as it coasts to a stop at constant angular deceleration. A) Through what total angle did the wheel turn between t=0 and the time it stopped? Express your answer in radians. B) At...
A wheel has an initial angular velocity of 1 rad/s and undergoes an angular acceleration of...
A wheel has an initial angular velocity of 1 rad/s and undergoes an angular acceleration of 10 rad/s^2. (a) How many radians does it rotate in 4 sec? (b) What is its angular velocity at this time?
22. A wheel, orginally rotating at 125 rad/s undergoes a constant angular deceleration of 5.00 rad/s^2....
22. A wheel, orginally rotating at 125 rad/s undergoes a constant angular deceleration of 5.00 rad/s^2. What is its angular speed after it has turned through an angle of 522 radians? 19. When you are out for a shopping, you noticed that the digitial sign outside the shopping center reports that the temperature is 43•C. What is the temperature in degrees Fahrenheit ? 16. A 77 -N •m torque acts on a wheel with a moment if inertia 175 kg...
1. A flywheel is initially rotating at 30 rad/s and has a constant angular acceleration. After...
1. A flywheel is initially rotating at 30 rad/s and has a constant angular acceleration. After 8.0 s it has rotated through 460 rad. Its angular acceleration in rad/s is: 2.Ten seconds after an electric fan is turned on, the fan rotates at 6000 rev/min. Its average angular acceleration in rad/s2 is: 3.The rotational inertia of a disk about its axis is 0.70 kgˑm2. When a 2.0-kg weight is added to its rim, 0.50 m from the axis, the rotational...
A gear has an angular velocity equal to 20 rad/s initially, but it speeds up to...
A gear has an angular velocity equal to 20 rad/s initially, but it speeds up to 40 rad/s in 5.0 seconds, while experiencing angular acceleration that is constant. Compute the number of turns the gear has undergone during those 5.0 seconds? 28 32 52 39 20 24
A wheel of radius 8 inches is rotating 15°/s. What is the linear speed v, the angular speed in RPM, and the angular speed in rad/s?
A wheel of radius 8 inches is rotating 15°/s. What is the linear speed v, the angular speed in RPM, and the angular speed in rad/s?
A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz...
A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 19.0 s . We have taken counterclockwise rotation to be positive. How long is the time interval during which the speed of the wheel is increasing?
a.) Calculate the angular velocity (in rad/s) of the Earth in its orbit around the sun...
a.) Calculate the angular velocity (in rad/s) of the Earth in its orbit around the sun and that about its axis. b.) Calculate the moment of inertia, the angular momentum, and the rotational kinetic energies for both cases.
A person is riding a bicycle, and its wheels have an angular velocity of 22.0 rad/s....
A person is riding a bicycle, and its wheels have an angular velocity of 22.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 12.9 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT