MCQs: Angular acceleration

1. An unbalanced torque acts on a disc that is at rest. After 5 s the disc is rotating at 2 revolutions per second. How many revolutions has the disc made

ωi = 0 rad s-1

ωf= 4π rad s-1

t = 5 s

θ = (ωi + ωf)t/2 = 4π x 5 /2 = 10 π = 5 revs

2. An unbalanced torque causes a disc rotating at 2 rad s-1 to accelerate at 4 rad s-2. How many rotations will the disc make in 5s?

ϑ space equals space omega subscript o space t plus space bevelled fraction numerator 1 over denominator 2 alpha t squared end fraction

θ = 2 x 5 + 1/2 x 4 x 52 = 60 rads = 60/2π revs

3. The wheels of a car are rotating at 4 rev s-1 . The brakes cause the wheel to stop rotating after 6 rotations. The time taken to stop the wheel is.

ωi = 4 x 2π rad s-1

ωf = 0 rad s-1

θ = 6 x 2π rads

θ = (ωi + ωf)t/2

t = 2θ/(ωi + ωf) = 24π/8π = 3 s

 

4. A wheel is pushed with a constant unbalanced torque so that it acheives an angular velocity of 20 rad s-1 in 5 s. Calculate the angular acceleration.

α = (ωf - ωi)/t = (20 - 0)/5 = 4 rad s-1

5. A wheel rotating at 4 rad s-1 is accelerated to 12 rad s-1 after rotating 32 rad. The angular acceleration is.

ωf2 = ωi2 + 2αθ 

α = (ωf2 - ωi2)/2θ = (122 - 42)/64 = 2 rad s-2

6. The graph below represents the angular motion of a body.

The number of revolutions made in 10 s is.

from graph angle = 20π = 10 revs

7. The graph below represents the rotation of a rigid body

The angular acceleration of the body is

constant gradient implies constant velocity

8. The graph below represents then rotation of a rigid body

The angular displacement of the body in 10 s is

100 rad

450 rad

200 rad

225 rad

Displacement = area under graph = 1/2 x 20 x 10

9. A mass moves in a circle on the end of a 20 cm long string. If the tangential velocity is 20 m s-1 how many cycles will it complete per second?

16

10

1.6

5

circumference = 2πr = 2π x 0.2 = 0.4π

time for one rev = cirumference/speed = 0.4π/20  number of cycles per second = 20/0.4π = 16

 

10. An unbalanced torque causes the body shown to rotate about point A.

If the rotational acceleration of point Y is 9 rad s-2 the angular acceleration of point X will be.

all points on a rigid body have the same angular acceleration

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