A wheel rotates with a constant angular acceleration of 3.25 rad/s 2 . Assume th

Question

A wheel rotates with a constant angular acceleration of 3.25 rad/s2. Assume the angular speed of the wheel is 2.30 rad/s at ti = 0. (a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad
  
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rev

(b) What is the angular speed of the wheel at t = 2.00 s?

Use the values from PRACTICE IT to help you work this exercise. (c) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.00 s.

Sketch the angular speed of the wheel as a function of time. What is its initial value? What does the slope represent? What does the area underneath it represent? rad

(d) Find the angular speed when t = 3.00 s.
rad/s A wheel rotates with a constant angular acceleration of 3.25 rad/s2. Assume the angular speed of the wheel is 2.30 rad/s at ti = 0. (a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad
  
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rev

(b) What is the angular speed of the wheel at t = 2.00 s?
A wheel rotates with a constant angular acceleration of 3.25 rad/s2. Assume the angular speed of the wheel is 2.30 rad/s at ti = 0. (a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad
  
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rev

(b) What is the angular speed of the wheel at t = 2.00 s?
(a) Through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and revolutions.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rad
  
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. rev

(b) What is the angular speed of the wheel at t = 2.00 s?

Use the values from PRACTICE IT to help you work this exercise. (c) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.00 s.

Sketch the angular speed of the wheel as a function of time. What is its initial value? What does the slope represent? What does the area underneath it represent? rad

(d) Find the angular speed when t = 3.00 s.
rad/s Use the values from PRACTICE IT to help you work this exercise. (c) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.00 s.

Sketch the angular speed of the wheel as a function of time. What is its initial value? What does the slope represent? What does the area underneath it represent? rad

(d) Find the angular speed when t = 3.00 s.
rad/s (c) Find the angle through which the wheel rotates between t = 2.00 s and t = 3.00 s.

Sketch the angular speed of the wheel as a function of time. What is its initial value? What does the slope represent? What does the area underneath it represent? rad

(d) Find the angular speed when t = 3.00 s.
rad/s

Explanation / Answer

Given Constant angular acceleration on wheel = 3.25 rad /s2 Angular speed of the wheel   i   = 2.3 rad /s a) Angle does the wheel rotate between t = 0 and t = 2.00 s is                         = i t + ( 1 /2 ) t 2                               = ( 2.3 rad /s ) ( 2.00 s ) + ( 0.5 ) ( 3.25 rad /s 2 ) ( 2.00 s )2                                 = 11.1 rad. ________________________________________________________________ b) Angular speed of the wheel at t = 2.00 s is                        = i + t                            = ( 2.3 rad /s ) + ( 3.25 rad/s2 ) ( 2.00 s )                            = 8.8 rad /s ________________________________________________________________ d) Angular speed of the wheel at t = 3.00 s is                     f = i + t                          = ( 2.3 rad /s ) + ( 3.25 rad /s2 ) ( 3.00 s )                           = 12.05 rad /s ________________________________________________________________ c) angle through which the wheel rotates between t = 2.00 s and t = 3.00 s                   f2 - 2   = 2                   ( 12.05 ) 2 - ( 8.8 )2 = 2 ( 3.25 rad /s2 )                         = 10.425 rad ________________________________________________________________ b) Angular speed of the wheel at t = 2.00 s is                        = i + t                            = ( 2.3 rad /s ) + ( 3.25 rad/s2 ) ( 2.00 s )                            = 8.8 rad /s ________________________________________________________________ d) Angular speed of the wheel at t = 3.00 s is                     f = i + t                          = ( 2.3 rad /s ) + ( 3.25 rad /s2 ) ( 3.00 s )                           = 12.05 rad /s ________________________________________________________________ c) angle through which the wheel rotates between t = 2.00 s and t = 3.00 s                   f2 - 2   = 2                   ( 12.05 ) 2 - ( 8.8 )2 = 2 ( 3.25 rad /s2 )                         = 10.425 rad

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