Question

In: Physics

A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end...

A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end of the 2.97-s interval is 97.0 rad/s. What is the constant angular acceleration of the wheel? _____ rad/s2

Expert Solution

Time period = T = 2.97 sec

Number of revolutions = n = 37 rev

Angle through which the wheel rotated =

= 2n

= 2(37)

= 232.478 rad

Initial angular speed of the wheel = ₁

Final angular speed of the wheel = ₂ = 97 rad/s

Angular acceleration of the wheel =

₂ = ₁ + T

₁ = ₂ - T

= ₁T + T²/2

= (₂ - T)T + T²/2

= ₂T - T² + T²/2

= ₂T - T²/2

232.478 = (97)(2.97) - (2.97)²/2

= 12.61 rad/s²

Constant angular acceleration of the wheel = 12.61 rad/s²

genius_generous answered 2 years ago

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 steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of...

A steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of 14.5 rad/s. The temperature of the wheel changes from -142 to 244 °C. No net external torque acts on the wheel, and the mass of the spokes is negligible. What is the angular speed of the wheel at the higher temperature?

A wheel, released from rest, is rotating with constant angular acceleration. After 8.0 seconds, its speed...

A wheel, released from rest, is rotating with constant angular acceleration. After 8.0 seconds, its speed reaches to 12 rev/sec (a) what is its angular acceleration? (b) Through what angle has the wheel turned? (c) How many revolutions has it completed in 8.0 second?

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?

A wheel is rotating freely at angular speed 530 rev/min on a shaft whose rotational inertia...

A wheel is rotating freely at angular speed 530 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with 5 times the rotational inertia of the first, is suddenly coupled to the same shaft. (a) What is the angular speed of the resultant combination of the shaft and two wheels? (b) What fraction of the original rotational kinetic energy is lost?

The angular position of a point on the rim of a rotating wheel is given by...

The angular position of a point on the rim of a rotating wheel is given by θ = 9.33t - 3.93t2 + 1.09t3, where θ is in radians and t is in seconds. What are the angular velocities at (a) t = 2.13 s and (b) t = 8.41 s? (c) What is the average angular acceleration for the time interval that begins at t = 2.13 s and ends at t = 8.41 s? What are the instantaneous angular...

A wheel turns through 2.1 revolutions while accelerating from rest at 16 rpm/s. What is its...

A wheel turns through 2.1 revolutions while accelerating from rest at 16 rpm/s. What is its final angular speed? How long does it take?

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...

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of...

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of the wheel is 2 rad/s at t = 0, through what angular displacement does the wheel rotate in 2 s? 10 rad. 6 rad. 15 rad. 4 rad. 12 rad. Based on question number 3, through how many revolutions has the wheel turned during this time interval? 4 rev. 3 rev. 1.6 rev. 5 rev. 2 rev. Based on question number 3, what is...

The wheel of an engine starts to rotate from rest with uniform angular acceleration. It accelerates...

The wheel of an engine starts to rotate from rest with uniform angular acceleration. It accelerates angularly for an unknown time (t1) until reaching an angular velocity of 45.13 rad / s, then maintains that angular velocity constant for 37.8 s. The total angle traveled by the wheel in total is 2398.61 rad. a) What is the angular acceleration with which the wheel began to rotate? b) What is the time (t1) that the wheel was accelerating? c) What is...